Relevant bibliographies by topics / Bifurcation and Chaos theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Bifurcation and Chaos theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Bifurcation and Chaos theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Bifurcation and Chaos theory"

1

Yang, Ting. "Multistability and Hidden Attractors in a Three-Dimensional Chaotic System." International Journal of Bifurcation and Chaos 30, no. 06 (May 2020): 2050087. http://dx.doi.org/10.1142/s021812742050087x.

Full text
Abstract:
This paper proposes a novel three-dimensional autonomous chaotic system. Interestingly, when the system has infinitely many stable equilibria, it is found that the system also has infinitely many hidden chaotic attractors. We show that the period-doubling bifurcations are the routes to chaos. Moreover, the Hopf bifurcations at all equilibria are investigated and it is also found that all the Hopf bifurcations simultaneously occur. Furthermore, the approximate expressions and stabilities of bifurcating limit cycles are obtained by using normal form theory and bifurcation theory.
APA, Harvard, Vancouver, ISO, and other styles
2

PENG, MINGSHU, and YUAN YUAN. "STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS." International Journal of Bifurcation and Chaos 18, no. 05 (May 2008): 1477–501. http://dx.doi.org/10.1142/s0218127408021117.

Full text
Abstract:
In this paper, we use the standard bifurcation theory to study rich dynamics of time-delayed coupling discrete oscillators. Equivariant bifurcations including equivariant Neimark–Sacker bifurcation, equivariant pitchfork bifurcation and equivariant periodic doubling bifurcation are analyzed in detail. In the application, we consider a ring of identical discrete delayed Ikeda oscillators. Multiple oscillation patterns, such as multiple stable equilibria, stable limit cycles, stable invariant tori and multiple chaotic attractors, are shown.
APA, Harvard, Vancouver, ISO, and other styles
3

Chen, Qin, and Jianguo Gao. "Delay Feedback Control of the Lorenz-Like System." Mathematical Problems in Engineering 2018 (June 28, 2018): 1–13. http://dx.doi.org/10.1155/2018/1459272.

Full text
Abstract:
We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.
APA, Harvard, Vancouver, ISO, and other styles
4

Liu, Yongjian, Xiezhen Huang, and Jincun Zheng. "Chaos and bifurcation in the controlled chaotic system." Open Mathematics 16, no. 1 (November 3, 2018): 1255–65. http://dx.doi.org/10.1515/math-2018-0105.

Full text
Abstract:
AbstractIn this paper, chaos and bifurcation are explored for the controlled chaotic system, which is put forward based on the hybrid strategy in an unusual chaotic system. Behavior of the controlled system with variable parameter is researched in detain. Moreover, the normal form theory is used to analyze the direction and stability of bifurcating periodic solution.
APA, Harvard, Vancouver, ISO, and other styles
5

XU, XU, HAIYAN HU, and HUAILEI WANG. "DYNAMICS OF A TWO-DIMENSIONAL DELAYED SMALL-WORLD NETWORK UNDER DELAYED FEEDBACK CONTROL." International Journal of Bifurcation and Chaos 16, no. 11 (November 2006): 3257–73. http://dx.doi.org/10.1142/s021812740601677x.

Full text
Abstract:
This paper presents a detailed analysis on the dynamics of a two-dimensional delayed small-world network under delayed state feedback control. On the basis of stability switch criteria, the equilibrium is studied, and the stability conditions are determined. This study shows that with properly chosen delay and gain in the delayed feedback path, the controlled small-world delayed network may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or the multistability solutions via three types of codimension two bifurcations. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are determined by using the normal form theory and center manifold theorem. In addition, the study shows that the controlled model exhibits period-doubling bifurcations which lead eventually to chaos; and the chaos can also directly occur via the bifurcations from the quasi-periodic solutions. The results show that the delayed feedback is an effective approach in order to generate or annihilate complex behaviors in practical applications.
APA, Harvard, Vancouver, ISO, and other styles
6

LI, CHUNGUANG, GUANRONG CHEN, XIAOFENG LIAO, and JUEBANG YU. "HOPF BIFURCATION AND CHAOS IN TABU LEARNING NEURON MODELS." International Journal of Bifurcation and Chaos 15, no. 08 (August 2005): 2633–42. http://dx.doi.org/10.1142/s0218127405013575.

Full text
Abstract:
In this paper, we consider the nonlinear dynamical behaviors of some tabu learning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. We give a numerical example to verify the theoretical analysis. Then, we demonstrate the chaotic behavior in such a neuron with sinusoidal external input, via computer simulations. Finally, we study the chaotic behaviors in tabu learning two-neuron models, with linear and quadratic proximity functions respectively.
APA, Harvard, Vancouver, ISO, and other styles
7

HARRISON, MARY ANN, and YING-CHENG LAI. "BIFURCATION TO HIGH-DIMENSIONAL CHAOS." International Journal of Bifurcation and Chaos 10, no. 06 (June 2000): 1471–83. http://dx.doi.org/10.1142/s0218127400000967.

Full text
Abstract:
High-dimensional chaos has been an area of growing recent investigation. The questions of how dynamical systems become high-dimensionally chaotic with multiple positive Lyapunov exponents, and what the characteristic features associated with the transition are, remain less investigated. In this paper, we present one possible route to high-dimensional chaos. By this route, a subsystem becomes chaotic with one positive Lyapunov exponent via one of the known routes to low-dimensional chaos, after which the complementary subsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the additional Lyapunov exponents pass through zero smoothly. As a consequence, the fractal dimension of the chaotic attractor changes continuously through the transition, in contrast to the transition to low-dimensional chaos at which the fractal dimension changes abruptly. We present a heuristic theory and numerical examples to illustrate this route to high-dimensional chaos.
APA, Harvard, Vancouver, ISO, and other styles
8

Abbasi, Muhammad Aqib, and Qamar Din. "Under the influence of crowding effects: Stability, bifurcation and chaos control for a discrete-time predator–prey model." International Journal of Biomathematics 12, no. 04 (May 2019): 1950044. http://dx.doi.org/10.1142/s179352451950044x.

Full text
Abstract:
The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey–predator model is investigated. Particularly, we examine the boundedness as well as existence and uniqueness of positive steady-state and stability analysis of the unique positive steady-state. Moreover, it is also proved that the system undergoes Hopf bifurcation and flip bifurcation with the help of bifurcation theory. Moreover, a chaos control technique is proposed for controlling chaos under the influence of bifurcations. Finally, numerical simulations are provided to illustrate the theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The presence of chaotic behavior in the model is confirmed by computing maximum Lyapunov exponents.
APA, Harvard, Vancouver, ISO, and other styles
9

Chen, Qiaoling, Zhidong Teng, and Zengyun Hu. "Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response." International Journal of Applied Mathematics and Computer Science 23, no. 2 (June 1, 2013): 247–61. http://dx.doi.org/10.2478/amcs-2013-0019.

Full text
Abstract:
The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.
APA, Harvard, Vancouver, ISO, and other styles
10

Rotshtein, Alexander, Denys Katielnikov, and Ludmila Pustylnik. "Reliability Modeling and Optimization Using Fuzzy Logic and Chaos Theory." International Journal of Quality, Statistics, and Reliability 2012 (October 23, 2012): 1–9. http://dx.doi.org/10.1155/2012/847416.

Full text
Abstract:
Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Bifurcation and Chaos theory"

1

Hyde, Griffin Nicholas. "Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/91395.

Full text
Abstract:
This thesis details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, indicating the onset of chaotic motion. These results are compared to simulation results, which suggest chaotic motion through the appearance of strange attractors in the Poincaré maps. Additionally, evidence of the WPP system experiencing both types of chaos simultaneously was found, resulting in a merger of two distinct types of strange attractor.
Master of Science
This report details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This system can be used to investigate what are known as local and global bifurcations. A local bifurcation occurs when the single equilibrium state (corresponding to the pendulum hanging straight down) when spun at low speeds, bifurcates into three equilibria when the spin rate is increased beyond a certain value. The global bifurcations occur when the system experiences sinusoidal forcing near certain equilibrium conditions. The resulting chaotic oscillations are investigated using Melnikov’s method, which determines when the sinusoidal forcing results in chaotic motion. This chaotic motion comes in two types, which cause the system to behave in different ways. Melnikov’s method, and results from a simulation were used to determine the parameter values in which the pendulum experiences each type of chaos. It was seen that at certain parameter values, the WPP experiences both types of chaos, supporting the observation that these types of chaos are not necessarily independent of each other, but can merge and interact.
APA, Harvard, Vancouver, ISO, and other styles
2

Natsheh, Ammar Nimer. "Analysis, simulation and control of chaotic behaviour and power electronic converters." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/5739.

Full text
Abstract:
The thesis describes theoretical and experimental studies on the chaotic behaviour of a peak current-mode controlled boost converter, a parallel two-module peak current-mode controlled DC-DC boost converter, and a peak current-mode controlled power factor correction (PFC) boost converter. The research concentrates on converters which do not have voltage control loops, since the main interest is in the intrinsic mechanism of chaotic behaviour. These converters produce sub-harmonics of the clock frequency at certain values of the reference current I[ref] and input voltage V[in], and may behave in a chaotic manner, whereby the frequency spectrum of the inductor becomes continuous. Non-linear maps for each of the converters are derived using discrete time modelling and numerical iteration of the maps produce bifurcation diagrams which indicate the presence of subharmonics and chaotic operation. In order to check the validity of the analysis, MATLAB/SIMULINK models for the converters are developed. A comparison is made between waveforms obtained from experimental converters, with those produced by the MATLAB/SIMULINK models of the converters. The experimental and theoretical results are also compared with the bifurcation points predicted by the bifurcation diagrams. The simulated waveforms show excellent agreement, with both the experimental waveforms and the transitions predicted by the bifurcation diagrams. The thesis presents the first application of a delayed feedback control scheme for eliminating chaotic behaviour in both the DC-DC boost converter and the PFC boost converter. Experimental results and FORTRAN simulations show the effectiveness and robustness of the scheme. FORTRAN simulations are found to be in close agreement with experimental results and the bifurcation diagrams. A theoretical comparison is made between the above converters controlled using delayed feedback control and the popular slope compensation method. It is shown that delayed feedback control is a simpler scheme and has a better performance than that for slope compensation.
APA, Harvard, Vancouver, ISO, and other styles
3

Guo, Yu. "BIFURCATION AND CHAOS OF NONLINEAR VIBRO-IMPACT SYSTEMS." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/dissertations/725.

Full text
Abstract:
Vibro-impact systems are extensively used in engineering and physics field, such as impact damper, particle accelerator, etc. These systems are most basic elements of many real world applications such as cars and aircrafts. Such vibro-impact systems possess both the continuous characteristics as continuous dynamical systems and discrete characteristics introduced by impacts at the same time. Thus, an appropriately developed discrete mapping system is required for such vibro-impact systems in order to simplify investigation on the complexity of motions. In this dissertation, a few vibro-impact oscillators will be investigated using discrete maps in order to understand the dynamics of vibro-impact systems. Before discussing the nonlinear dynamical phenomena and behaviors of these vibro-impact oscillators, the theory for nonlinear discrete systems will be applied to investigate a two-dimensional discrete system (Henon Map). And the complete dynamics of such a nonlinear discrete dynamical system will be presented using the inversed mapping method. Neimark bifurcations in such a discrete system have also drawn a lot of interest to the author. The Neimark bifurcations in such a system have actually formed a boundary dividing the stable solution of positive and negative maps (inversed mapping). For the first time, one is able to obtain a complete prediction of both stable and unstable solutions in such a discrete dynamical system. And a detailed parameter map will be presented to illustrate how changes of parameters could affect the different solutions in such a system. Then, the theory of discontinuous dynamical systems will be adopted to investigate the vibro-impact dynamics in several vibro-impact systems. First, the bouncing ball dynamics will be analytically discussed using a single discrete map. Different types of motions (periodic and chaotic) will be presented to understand the complex behavior of this simple model. Analytical condition will be expressed using switching phase of the system in order to easily predict stick and grazing motion. After that, a horizontal impact damper model will be studied to show how complex periodic motions could be developed analytically. Complete set of symmetric and asymmetric periodic motions can also be easily predicted using the analytical method. Finally, a Fermi-Accelerator being excited at both ends will be discussed in detail for application. Different types of motions will be thoroughly studied for such a vibro-impact system under both same and different excitations.
APA, Harvard, Vancouver, ISO, and other styles
4

Kumeno, Hironori. "Bifurcation and Synchronization in Parametrically Forced Systems." Thesis, Toulouse, INSA, 2012. http://www.theses.fr/2012ISAT0024/document.

Full text
Abstract:
Dans cette thèse, nous étudions un système à temps discret de dimension N, dont les paramètres varient périodiquement. Le système de dimension N est construit à partir de n sous-systèmes de dimension un couplés symétriquement. Dans un premier temps, nous donnons les propriétés générales du système de dimension N. Dans un second temps, nous étudions le cas particulier où le sous-système de dimension un est défini à l’aide d’une transformation logistique. Nous nous intéressons plus particulièrement à la structure des bifurcations lorsque N=1 ou 2. Des zones échangeurs centrées sur des points cuspidaux sont obtenues dans le cas de courbes de bifurcation de type fold (noeud-col).Ensuite, nous nous intéressons au comportement de circuits de type Chua couplés lorsqu’un paramètre varie lui aussi périodiquement, la période étant celle d’une des variables d’état interne au système. A partir de l’étude des bifurcations du système, la non existence de cycles d’ordre impair et la coexistence de plusieurs attracteurs est mise en évidence. D’autre part, on peut mettre en évidence la coexistence de différents attracteurs pour lesquels les états de synchronisation sont distincts. Le cas continu est comparé avec le cas discret. Des phénomènes tout à fait similaires sont obtenus. Il est important de noter que l’étude d’un système à temps discret est plus facile et plus rapide que celle d’un système à temps continu. L’étude du premier système permet donc d’avoir des informations sur ce qui peut se produire dans le cas continu. Pour terminer, nous analysons le comportement d’un autre système couplé à temps continu, basé lui aussi sur le circuit de Chua, mais pour lequel la commutation qui contrôle la variation du paramètre s’effectue différemment du premier système. Ce type de commutation génère une augmentation du nombre d’attracteurs
In this thesis, we propose a N-dimensional coupled discrete-time system whose parameters are forced into periodic varying, the N-dimensional system being constructed of n same one-dimensional subsystems with mutually influencing coupling and also coupled continuous-time system including periodically parameter varying which correspond to the periodic varying in the discrete-time system.Firstly, we introduce the N-dimensional coupled parametrically forced discrete-time system and its general properties. Then, when logistic maps is used as the one-dimensional subsystem constructing the system, bifurcations in the one or two-dimensional parametrically forced logistic map are investigated. Crossroad area centered at fold cusp points regarding several order cycles are confirmed.Next, we investigated behaviors of the coupled Chua's circuit whose parameter is forced into periodic varying associated with the period of an internal state value. From the investigation of bifurcations in the system, non-existence of odd order cycles and coexistence of different attractors are observed. From the investigation of synchronizations coexisting of many attractors whose synchronizations states are different are observed. Observed phenomena in the system is compared with the parametrically forced discrete-time system. Similar phenomena are confirmed between the parametrically forced discrete-time system and the parametrically forced Chua's circuit. It is worth noting that this facilitates to analyze parametrically forced continuous-time systems, because to analyze discrete-time systems is easier than continuous-time systems. Finally, we investigated behaviors of another coupled continuous-time system in which Chua's circuit is used, while, the motion of the switch controlling the parametric varying is different from the above system. Coexisting of many attractors whose synchronizations states are different are observed. Comparing with theabove system, the number of coexisting stable state is increased by the effect of the different switching motion
APA, Harvard, Vancouver, ISO, and other styles
5

Abashar, Mohd Elbashir E. "Bifurcation, instability and chaos in fluidized bed catalytic reactors." Thesis, University of Salford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386532.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Salih, Rizgar Haji. "Hopf bifurcation and centre bifurcation in three dimensional Lotka-Volterra systems." Thesis, University of Plymouth, 2015. http://hdl.handle.net/10026.1/3504.

Full text
Abstract:
This thesis presents a study of the centre bifurcation and chaotic behaviour of three dimensional Lotka-Volterra systems. In two dimensional systems, Christopher (2005) considered a simple computational approach to estimate the cyclicity bifurcating from the centre. We generalized the technique to estimate the cyclicity of the centre in three dimensional systems. A lower bounds is given for the cyclicity of a hopf point in the three dimensional Lotka-Volterra systems via centre bifurcations. Sufficient conditions for the existence of a centre are obtained via the Darboux method using inverse Jacobi multiplier functions. For a given centre, the cyclicity is bounded from below by considering the linear parts of the corresponding Liapunov quantities of the perturbed system. Although the number obtained is not new, the technique is fast and can easily be adapted to other systems. The same technique is applied to estimate the cyclicity of a three dimensional system with a plane of singularities. As a result, eight limit cycles are shown to bifurcate from the centre by considering the quadratic parts of the corresponding Liapunov quantities of the perturbed system. This thesis also examines the chaotic behaviour of three dimensional Lotka-Volterra systems. For studying the chaotic behaviour, a geometric method is used. We construct an example of a three dimensional Lotka-Volterra system with a saddle-focus critical point of Shilnikov type as well as a loop. A construction of the heteroclinic cycle that joins the critical point with two other critical points of type planar saddle and axial saddle is undertaken. Furthermore, the local behaviour of trajectories in a small neighbourhood of the critical points is investigated. The dynamics of the Poincare map around the heteroclinic cycle can exhibit chaos by demonstrating the existence of a horseshoe map. The proof uses a Shilnikov-type structure adapted to the geometry of these systems. For a good understanding of the global dynamics of the system, the behaviour at infinity is also examined. This helps us to draw the global phase portrait of the system. The last part of this thesis is devoted to a study of the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems. Explicit conditions for the existence of two first integrals for the system and a line of singularity with zero eigenvalue are given. We characteristic the parameters for which a zero-Hopf equilibrium point takes place at any points on the line. We prove that there are three 3-parameter families exhibiting such equilibria. First order of averaging theory is also applied but we show that it gives no information about the possible periodic orbits bifurcating from the zero-Hopf equilibria.
APA, Harvard, Vancouver, ISO, and other styles
7

Hughes, Ryan Patrick. "Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96567.

Full text
Abstract:
Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not.
Master of Science
Often times biological processes do not happen in a continuous streamlined chain of events. We observe discrete life stages, ages, and morphological differences. Similarly, data is generally collected in discrete (and often fixed) time intervals. This work focuses on the role that population density has on the behavior of these systems. We dive into a case study for a viral infection in a salmon population. We show chaotic behavior can be observed as low as a single dimension model and discuss the biological implications. Additionally, we show that the choice of density dependence in a given infectious disease model directly impacts disease dynamics and can allow or prohibit chaotic behavior.
APA, Harvard, Vancouver, ISO, and other styles
8

Gaunersdorfer, Andrea, Cars H. Hommes, and Florian O. O. Wagener. "Bifurcation routes to volatility clustering." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/522/1/document.pdf.

Full text
Abstract:
A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems. (author's abstract)
Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
APA, Harvard, Vancouver, ISO, and other styles
9

Welsh, S. C. "Generalised topological degree and bifurcation theory." Thesis, University of Glasgow, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372419.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

何振林 and Albert Ho. "Chaos theory and security analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31264931.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Bifurcation and Chaos theory"

1

T, Leung A. Y., ed. Bifurcation and chaos in engineering. London: Springer, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Chen, Yushu. Bifurcation and Chaos in Engineering. London: Springer London, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Bifurcation and chaos in coupled oscillators. Singapore: World Scientific, 1991.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Seydel, R. Practical bifurcation and stability analysis: From equilibrium to chaos. 2nd ed. New York: Springer-Verlag, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Seydel, R. Practical bifurcation and stability analysis: From equilibrium to chaos. 2nd ed. New York: Springer-Verlag, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Awrejcewicz, J. Bifurcation and chaos in nonsmooth mechanical systems. Singapore: World Scientific, 2004.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Claude-Henri, Lamarque, ed. Bifurcation and chaos in nonsmooth mechanical systems. River Edge, NJ: World Scientific, 2003.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Bifurcation and chaos in simple dynamical systems. Singapore: World Scientific, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Sparrow, Colin. The Lorenz equations: Bifurcations, chaos, and strange attractors. Mineola, NY: Dover Publications, 2005.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Seydel, R. From equilibrium to chaos: Practical bifurcation and stability analysis. New York: Elsevier, 1988.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Bifurcation and Chaos theory"

1

Argyris, John, Gunter Faust, Maria Haase, and Rudolf Friedrich. "Local Bifurcation Theory." In An Exploration of Dynamical Systems and Chaos, 299–434. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46042-9_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Chen, Yushu, and Andrew Y. T. Leung. "Application of the Averaging Method in Bifurcation Theory." In Bifurcation and Chaos in Engineering, 230–64. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-1575-5_7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Bayliss, Alvin, and Bernard J. Matkowsky. "Bifurcation, Pattern Formation and Chaos in Combustion." In Dynamical Issues in Combustion Theory, 1–35. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0947-8_1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Kirchgraber, U., F. Lasagni, K. Nipp, and D. Stoffer. "On the Application of Invariant Manifold Theory, in particular to Numerical Analysis." In Bifurcation and Chaos: Analysis, Algorithms, Applications, 189–97. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7004-7_23.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Barnett, William A., and Yijun He. "Nonlinearity, Chaos, and Bifurcation: A Competition and an Experiment." In Economic Theory, Dynamics and Markets, 167–87. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1677-4_13.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Ichiro, Ario. "Multiple Duffing Problems Based on Hilltop Bifurcation Theory on MFM Models." In Handbook of Applications of Chaos Theory, 719–42. Boca Ration : Taylor & Francis, 2016.|“A CRC title.”: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/b20232-35.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Layek, G. C. "Theory of Bifurcations." In An Introduction to Dynamical Systems and Chaos, 203–54. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2556-0_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Nishiuchi, Yusuke, and Tetsushi Ueta. "Bifurcation Analysis of a Simple 3D BVP Oscillator and Chaos Synchronization of Its Coupled Systems." In Handbook of Applications of Chaos Theory, 145–54. Boca Ration : Taylor & Francis, 2016.|“A CRC title.”: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/b20232-9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Chen, Yushu, and Andrew Y. T. Leung. "Hopf Bifurcation." In Bifurcation and Chaos in Engineering, 176–229. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-1575-5_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Puu, Tönu. "Bifurcation and Catastrophe." In Attractors, Bifurcations, & Chaos, 217–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24699-2_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Bifurcation and Chaos theory"

1

Evan-lwanowski, R. M., and Chu-Ho Lu. "Transitions Through Period Doubling Route to Chaos." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0328.

Full text
Abstract:
Abstract The Duffing driven, damped, “softening” oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T… chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t)=Ω0±α2t,f=const., Ω-line, and along the E-line: Ω(t)=Ω0±α2t;f(t)=f0∓α2t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a, Ω) or (a, f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response x(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos — they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems.
APA, Harvard, Vancouver, ISO, and other styles
2

Zhang, Wei, Minghui Zhao, and Xiangying Guo. "Chaos and Bifurcation of Composite Laminated Cantilever Rectangular Plate." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70074.

Full text
Abstract:
According to the Reddy’s high-order shear deformation theory and the von-Karman type equations for the geometric nonlinearity, the chaos and bifurcation of a composite laminated cantilever rectangular plate subjected to the in-plane and moment excitations are investigated with the case of 1:2 internal resonance. A new expression of displacement functions which can satisfy the cantilever plate boundary conditions are used to make the nonlinear partial differential governing equations of motion discretized into a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations, representing the evolution of the amplitudes and phases exhibiting complex dynamics. The results of numerical simulation demonstrate that there exist the periodic and chaotic motions of the composite laminated cantilever rectangular plate. Finally, the influence of the forcing excitations on the bifurcations and chaotic behaviors of the system is investigated numerically.
APA, Harvard, Vancouver, ISO, and other styles
3

Kabiraj, Lipika, R. I. Sujith, and Pankaj Wahi. "Experimental Studies of Bifurcations Leading to Chaos in a Laboratory Scale Thermoacoustic System." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46149.

Full text
Abstract:
Bifurcation analysis is conducted on experimental data obtained from a simple setup comprising of ducted, laminar pre-mixed conical flames to investigate the features of nonlinear thermoacoustic oscillations. It is observed that as the bifurcation parameter is varied, the system undergoes series of bifurcations leading to characteristically different nonlinear oscillations. Through the application of nonlinear time series analysis on pressure and flame (CH* chemiluminescence) intensity time traces, these oscillations are characterised as periodic, aperiodic or chaotic oscillations and subsequently the nature of the obtained bifurcations is explained based on dynamical systems theory. Nonlinear interaction between the flames and the acoustic modes of the duct is clearly reflected in the high speed flame images acquired simultaneously with pressure and flame intensity measurements.
APA, Harvard, Vancouver, ISO, and other styles
4

Zhang, Wei, Feng-Hong Yang, and Bin Hu. "Sliding Bifurcations and Chaos in a Braking System." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34356.

Full text
Abstract:
In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree -of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick-slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing-sliding bifurcation and stick-slip chaos in the braking system.
APA, Harvard, Vancouver, ISO, and other styles
5

Luo, Albert C. J., and Yu Guo. "Switching Bifurcation and Chaos in an Extended Fermi-Acceleration Oscillator." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68003.

Full text
Abstract:
The Fermi acceleration oscillator is extensively used to interpret many physical and mechanical phenomena. To understand dynamic behaviors of a particle (or a bouncing ball) in such a Fermi oscillator, a generalized Fermi acceleration model is developed. This model consists of a particle moving vertically between a fixed wall and the piston in a vibrating oscillator. The motion switching bifurcation of a particle in such a generalized Fermi oscillator is investigated through the theory of discontinuous dynamical systems. The analytical conditions for the motion switching are developed for numerical predictions. Thus, periodic motions in the Fermi-acceleration oscillator are given and the corresponding local stability and bifurcation are presented. Periodic and chaotic motions in such an oscillator are presented via the displacement time-history. From switching bifurcation and period-doubling bifurcation, parameter maps of periodic and chaotic motions will be developed for a global view of motions in the Fermi acceleration oscillator. To illustrate motion switching phenomena, the acceleration responses of the particle and base in the Fermi oscillator are presented. Poincare mapping sections are also used to illustrate chaos, and energy dissipation in chaotic motions can be evaluated.
APA, Harvard, Vancouver, ISO, and other styles
6

Bondarenko, Alexander V., Alexander F. Glova, Sergei N. Kozlov, Fedor V. Lebedev, Vladimir V. Likhanskii, Anatoly P. Napartovich, Vladislav D. Pis'mennyi, and Vladimir P. Yartsev. "Bifurcation and chaos in a system of optically coupled CO2 lasers." In High-Power Multibeam Lasers and Their Phase Locking, edited by Fedor V. Lebedev and Anatoly P. Napartovich. SPIE, 1993. http://dx.doi.org/10.1117/12.160384.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Lefebvre, Tom, Frederik De Belie, and Guillaume Crevecoeur. "Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena." In 2018 22nd International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2018. http://dx.doi.org/10.1109/icstcc.2018.8540758.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Ashrafi, N., A. Hazbavi, and F. Forghani. "Chaos in Non-Newtonian Rotational Flow With Axial Flow." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85608.

Full text
Abstract:
The influence of axial flow on the vortex formation of pseudoplastic rotating flow between cylinders is explored. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In addition to the simulation of spiral flow, the proposed formulation allows the axial flow to be independent of the main rotating flow. Complete transient flow field together with viscosity maps are also presented.
APA, Harvard, Vancouver, ISO, and other styles
9

Guo, Yi, and Robert G. Parker. "Effects of Bearing Radial Internal Clearance on Dynamic Behavior and Bifurcations in Planetary Gears." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48891.

Full text
Abstract:
This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models of planetary gears with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc-length continuation is used to obtain the dynamic response of the lumped-parameter model. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited in the dynamic response, consisting of nonlinear jumps and a hardening effect induced by the transition from no bearing contact to contact. The bearings of the central members (sun, ring, and carrier) impact against the bearing races near resonance, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf bifurcation is the route to chaos. Input torque can significantly suppress the nonlinear effects caused by bearing clearance.
APA, Harvard, Vancouver, ISO, and other styles
10

Mureithi, N. W., K. Huynh, and A. Pham. "Low Order Model Dynamics of the Forced Cylinder Wake." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-78093.

Full text
Abstract:
The periodically forced cylinder wake exhibits complex but highly symmetrical patterns. In recent work, the authors have exploited symmetry-group equivariant bifurcation theory to derive low order equations describing, approximately, the dominant nonlinear dynamics of wake mode interactions. The models have been shown to qualitatively predict the observed bifurcations suggesting that the Karman wake remains, dynamically, a fairly simple system at least when viewed in 2D. Preliminary experimental data are presented supporting the feasibility of using 2D simulation results for the derivation of the low order model parameters. A POD analysis of the wake PIV velocity field yields flow modes closely similarly to those obtained via 2D CFD computations for Re in the 1000 range. The paper presents new results of simulations for Re = 200. For this low Reynolds number, the forced Karman wake exhibits rich dynamics dominated by quasi-periodicity, mode locking, torus doubling and chaos. The low Re torus breakdown may be explained by the Afraimovich-Shilnikov theorem. Interestingly, in a previous analysis for the higher Re number, Re = 1000, transition to a period-doubled flow state was found to occur via a route akin to the Takens-Bogdanov bifurcation scenario.
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Bifurcation and Chaos theory"

1

Crawford, J., C. Kueny, B. Saphir, and B. Shadwick. Introduction to bifurcation theory. Office of Scientific and Technical Information (OSTI), November 1989. http://dx.doi.org/10.2172/5396551.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Farhat, N. H. Cognitive Networks for ATR: The Roles of Bifurcation and Chaos. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada289010.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Farhat, Nabil H. Cognitive Networks for ATR: The Roles of Bifurcation and Chaos. Fort Belvoir, VA: Defense Technical Information Center, April 1995. http://dx.doi.org/10.21236/ada300342.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Mueller, Theodore H. Chaos Theory and the Mayaguez Crisis. Fort Belvoir, VA: Defense Technical Information Center, March 1990. http://dx.doi.org/10.21236/ada222901.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Durham, Susan E. Chaos Theory for the Practical Military Mind. Fort Belvoir, VA: Defense Technical Information Center, March 1997. http://dx.doi.org/10.21236/ada388495.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Dobson, Rhea E. Chaos Theory and the Effort in Afghanistan. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada478503.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Fote, A., S. Kohn, E. Fletcher, and J. McDonough. Application of Chaos Theory to 1/f Noise. Fort Belvoir, VA: Defense Technical Information Center, February 1988. http://dx.doi.org/10.21236/ada191150.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Mitchell, Glenn W. The New Math for Leaders: Useful Ideas from Chaos Theory. Fort Belvoir, VA: Defense Technical Information Center, March 1998. http://dx.doi.org/10.21236/ada345511.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Williford, R. E., and C. F. Jr Windisch. Final report on the application of chaos theory to an alumina sensor for aluminum reduction cells. Office of Scientific and Technical Information (OSTI), March 1992. http://dx.doi.org/10.2172/5638641.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Johnson, Darfus L. Wizards of Chaos and Order: A Theory of the Origins, Practice, And Future of Operational Art. Fort Belvoir, VA: Defense Technical Information Center, May 1999. http://dx.doi.org/10.21236/ada370245.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Bifurcation and Chaos theory' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography