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Thematische Bibliographien / Chaotic behavior in systems / Zeitschriftenartikel

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Zeitschriftenartikel zum Thema „Chaotic behavior in systems“

Autor: Grafiati

Veröffentlicht am 4. Juni 2021

Zuletzt aktualisiert am 29. Juli 2024

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1

HOLDEN, ARUN V., and MAX J. LAB. "Chaotic Behavior in Excitable Systems." Annals of the New York Academy of Sciences 591, no. 1 Mathematical (June 1990): 303–15. http://dx.doi.org/10.1111/j.1749-6632.1990.tb15097.x.

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2

Alfaro, Miguel D., and Juan M. Sepulveda. "Chaotic behavior in manufacturing systems." International Journal of Production Economics 101, no. 1 (May 2006): 150–58. http://dx.doi.org/10.1016/j.ijpe.2005.05.012.

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3

Wu, Xiaomao, and Z. A. Schelly. "Chaotic behavior of chemical systems." Reaction Kinetics and Catalysis Letters 42, no. 2 (September 1990): 303–7. http://dx.doi.org/10.1007/bf02065364.

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4

Wang, Tianyi. "Classification of Chaotic Behaviors in Jerky Dynamical Systems." Complex Systems 30, no. 1 (February 15, 2021): 93–110. http://dx.doi.org/10.25088/complexsystems.30.1.93.

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Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.

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5

YANG, XIAO-SONG, and LEI WANG. "EMERGENT PERIODIC BEHAVIOR IN COUPLED CHAOTIC SYSTEMS." Advances in Complex Systems 09, no. 03 (September 2006): 249–61. http://dx.doi.org/10.1142/s0219525906000793.

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Emergent behavior in interconnected systems (complex systems) is of fundamental significance in natural and engineering sciences. A commonly investigated problem is how complicated dynamics take place in dynamical systems consisting of (often simple) subsystems. It is shown though numerical experiments that emergent order such as periodic behavior can likely take place in coupled chaotic dynamical systems. This is demonstrated for the particular case of coupled chaotic continuous time Hopfield neural networks. In particular, it is shown that when two chaotic Hopfield neural networks are coupled by simple sigmoid signals, periodic behavior can emerge as a consequence of this coupling.

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VIANA, R. L., S. E. DE S. PINTO, J. R. R. BARBOSA, and C. GREBOGI. "PSEUDO-DETERMINISTIC CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3235–53. http://dx.doi.org/10.1142/s0218127403008636.

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We call a chaotic dynamical system pseudo-deterministic when it does not produce numerical, or pseudo-trajectories that stay close, or shadow chaotic true trajectories, even though the model equations are strictly deterministic. In this case, single chaotic trajectories may not be meaningful, and only statistical predictions, at best, could be drawn on the model, like in a stochastic system. The dynamical reason for this behavior is nonhyperbolicity characterized either by tangencies of stable and unstable manifolds or by the presence of periodic orbits embedded in a chaotic invariant set with a different number of unstable directions. We emphasize herewith the latter by studying a low-dimensional discrete-time model in which the phenomenon appears due to a saddle-repeller bifurcation. We also investigate the behavior of the finite-time Lyapunov exponents for the system, which quantifies this type of nonhyperbolicity as a system parameter evolves past a critical value. We argue that the effect of unstable dimension variability is more intense when the invariant chaotic set of the system loses transversal stability through a blowout bifurcation.

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Dewangan, Omprakash. "Machine Learning Approaches for Predicting Chaotic Behavior in Nonlinear Systems." Communications on Applied Nonlinear Analysis 30, no. 3 (December 27, 2023): 01–15. http://dx.doi.org/10.52783/cana.v30.275.

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In many domains, including biology, engineering, physics, and finance, the ability to forecast chaotic behavior is of the utmost importance. Predicting nonlinear systems accurately is a critical task due to their intrinsic sensitivity to initial conditions and lack of apparent patterns. One potential way to address this difficulty is by utilizing machine learning techniques. These methods can help us better understand and manage complex systems that display chaotic dynamics. Complex nonlinear systems, with their great dimensionality, temporal interdependence, and sensitivity to initial conditions, make chaotic behavior prediction difficult. The development of sophisticated tools that can detect patterns in chaotic dynamics is often necessary because traditional methods fail to capture these subtleties. The present research presents Chaotic Dynamics Prediction through Deep Ensemble Learning (CDP-DEL), an approach to chaotic dynamics prediction (CDP) that combines deep learning architectures with ensemble learning methodologies. Ensemble learning improves generalizability and reduces overfitting, whereas deep neural networks are made to capture complicated nonlinear interactions. CDP-DEL is an all-inclusive method for predicting chaotic behavior in nonlinear systems since it uses feature engineering, integrates system factors, and handles temporal dependencies. Among the many fields that have found use for CDP-DEL are control systems, ecological research, financial modeling, and weather forecasting. When applied to real-world scenarios with substantial chaotic dynamics repercussions, CDP-DEL's improved prediction capabilities may help optimize decision-making processes. Extensive simulation evaluations are performed utilizing benchmark chaotic systems to validate the efficacy of CDP-DEL. Research comparing CDP-DEL to more conventional methods show that it is more effective at predicting chaotic behavior and overall outperforms the competition.

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8

Wang, Z., S. Panahi, A. J. M. Khalaf, S. Jafari, and I. Hussain. "Synchronization of chaotic jerk systems." International Journal of Modern Physics B 34, no. 20 (August 5, 2020): 2050189. http://dx.doi.org/10.1142/s0217979220501891.

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Chaotic jerk oscillators belong to the simplest chaotic systems. These systems try to model the behavior of dynamical systems efficiently. Jerk oscillators can be known as the most general systems in science, especially physics. It has been proved that every dynamical system expressed with an ordinary differential equation is able to describe as a jerky system in particular conditions. One of its main topics is investigating the collective behavior of chaotic jerk oscillators in the dynamical network. In this paper, the synchronizability of the identical network of jerk oscillators is examined in three different coupling configurations, which are velocity, acceleration, and jerk coupling, and the results are compared with each other.

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Alessio, Francesca, Vittorio Coti Zelati, and Piero Montecchiari. "Chaotic behavior of rapidly oscillating Lagrangian systems." Discrete & Continuous Dynamical Systems - A 10, no. 3 (2004): 687–707. http://dx.doi.org/10.3934/dcds.2004.10.687.

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10

Zielinska, Barbara J. A., David Mukamel, Victor Steinberg, and Shmuel Fishman. "Chaotic behavior in externally modulated hydrodynamic systems." Physical Review A 32, no. 1 (July 1, 1985): 702–5. http://dx.doi.org/10.1103/physreva.32.702.

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11

Douka, Panagiota. "Chaotic behavior in discrete semi-dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 30, no. 1 (December 1997): 477–82. http://dx.doi.org/10.1016/s0362-546x(97)00275-7.

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12

Bambah, Bindu A., S. Lakshmibala, C. Mukku, and M. S. Sriram. "Chaotic behavior in Chern-Simons-Higgs systems." Physical Review D 47, no. 10 (May 15, 1993): 4677–87. http://dx.doi.org/10.1103/physrevd.47.4677.

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13

ERJAEE, G. H., M. H. ATABAKZADE, and L. M. SAHA. "INTERESTING SYNCHRONIZATION-LIKE BEHAVIOR." International Journal of Bifurcation and Chaos 14, no. 04 (April 2004): 1447–53. http://dx.doi.org/10.1142/s0218127404009934.

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We analyze the behavior of some coupled chaotic systems, which are synchronization-like. This phenomenon occurs when all conditional Lyapunov exponents of a system are not negative. Recently, Shuaiet et al. [1997] observed that synchronization can be achieved even with positive conditional Lyapunov exponents. In this paper we review this observation, and, based on this observation, we will see that not only interesting synchronization behaviors occur with positive or zero conditional Lyapunov exponents, but also these behaviors depend on different eigenvalues of the linearized system describing the evolution of the difference between the pair of chaotic systems.

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Chaté, Hugues. "Emergence of Collective Behavior in Large Chaotic Dynamical Systems." International Journal of Modern Physics B 12, no. 03 (January 30, 1998): 299–308. http://dx.doi.org/10.1142/s0217979298000235.

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The possibilities for observing the emergence of collective behavior in large chaotic dynamical systems are discussed. Nontrivial collective behavior in extensively-chaotic situations is presented with the help of a few examples and argued to offer all the desirable properties of a truly generic phenomenon.

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Wang, Chuanfu, and Qun Ding. "Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period." Complexity 2019 (December 22, 2019): 1–10. http://dx.doi.org/10.1155/2019/5942121.

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When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved efficiently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

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Jiménez-Casas, Ángela, Mario Castro, and Manuel Villanueva-Pesqueira. "The Role of Elasticity on Chaotic Dynamics: Insights from Mechanics, Immunology, Ecology, and Rheology." Mathematics 11, no. 14 (July 13, 2023): 3099. http://dx.doi.org/10.3390/math11143099.

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Elasticity is commonly associated with regular oscillations, which are prevalent in various systems at different scales. However, chaotic oscillations are rarely connected to elasticity. While overdamped chaotic systems have received significant attention, there has been limited exploration of elasticity-driven systems. In this study, we investigate the influence of elasticity on the dynamics of chaotic systems by examining diverse models derived from mechanics, immunology, ecology, and rheology. Through numerical MATLAB simulations obtained by using an ode15s solver, we observe that elasticity profoundly alters the chaotic dynamics of these systems. As a result, we term the underlying equations as the elastic-Lorenz equations. Specifically, we extensively analyze a viscoelastic fluid confined within a closed-loop thermosyphon, considering general heat flux, to demonstrate the impact of the viscoelastic parameter on the model’s chaotic behavior. Our findings build upon prior research on the asymptotic behavior of this model by incorporating the presence of a viscoelastic fluid. The results highlight the non-trivial and non-monotonic role of elasticity in understanding the control, or lack thereof, of chaotic behavior across different scales.

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Shah, Nehad Ali, Iftikhar Ahmed, Kanayo K. Asogwa, Azhar Ali Zafar, Wajaree Weera, and Ali Akgül. "Numerical study of a nonlinear fractional chaotic Chua's circuit." AIMS Mathematics 8, no. 1 (2023): 1636–55. http://dx.doi.org/10.3934/math.2023083.

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<abstract> <p>As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.</p> </abstract>

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Harb, Ahmad M., and Issam A. Smadi. "On Fuzzy Control of Chaotic Systems." Journal of Vibration and Control 10, no. 7 (July 2004): 979–93. http://dx.doi.org/10.1177/1077546304041541.

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In this paper, we introduce the control of the strange attractor, chaos. Because of the importance of controlling undesirable behavior in systems. researchers are investigating the use of linear and nonlinear controllers, either to remove such oscillations (in power systems) or to match two chaotic systems (in secure communications). The idea of using the fuzzy logic concept for controlling chaotic behavior is presented. There are two good reasons for using fulzy control: first, there is no mathematical model available for the process; secondly. it can satisfy nonlinear control that can be developed empirically. without complicated mathematics. The two systems are well-known models so the first reason is not a big problem. and we can take advantage of the second reason.

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USHIO, Toshimitsu, and Kazumasa HIRAI. "Chaotic Behavior in Pulse-Width Modulated Feedback Systems." Transactions of the Society of Instrument and Control Engineers 21, no. 6 (1985): 539–45. http://dx.doi.org/10.9746/sicetr1965.21.539.

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20

Islam Khan, Md Shariful. "Chaotic Behavior and Strange Attractors in Dynamical Systems." IOSR Journal of Mathematics 2, no. 5 (2012): 25–31. http://dx.doi.org/10.9790/5728-0252531.

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21

Loskutov, A. Yu, and A. R. Dzhanoev. "Stabilization of the chaotic behavior of dynamical systems." Doklady Physics 48, no. 10 (October 2003): 580–82. http://dx.doi.org/10.1134/1.1623542.

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22

Goldman, P., and A. Muszynska. "Chaotic Behavior of Rotor/Stator Systems With Rubs." Journal of Engineering for Gas Turbines and Power 116, no. 3 (July 1, 1994): 692–701. http://dx.doi.org/10.1115/1.2906875.

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This paper outlines the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions. The observed phenomena have one major source of a strong nonlinearity: transition from no contact to contact state between mechanical elements, one of which is rotating, resulting in variable stiffness and damping, impacting, and intermittent involvement of friction. A new model for such a transition (impact) is developed. In case of the contact between rotating and stationary elements, it correlates the local radial and tangential (“super ball”) effects with global behavior of the system. The results of numerical simulations of a simple rotor/stator system based on that model are presented in the form of bifurcation diagrams, rotor lateral vibration time-base waves, and orbits. The vibrational behavior of the system considered is characterized by orderly harmonic and subharmonic responses, as well as by chaotic vibrations. A new result is obtained in case of heavy rub of an anisotropically supported rotor. The system exhibits an additional subharmonic regime of vibration due to the stiffness asymmetry. The correspondence between numerical simulation of that effect and previously obtained experimental data supports the adequacy of the new model of impact.

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23

Ott, Edward, John C. Sommerer, James C. Alexander, Ittai Kan, and James A. Yorke. "Scaling behavior of chaotic systems with riddled basins." Physical Review Letters 71, no. 25 (December 20, 1993): 4134–37. http://dx.doi.org/10.1103/physrevlett.71.4134.

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24

Carnevale, G. F., M. Falcioni, S. Isola, R. Purini, and A. Vulpiani. "Fluctuation‐response relations in systems with chaotic behavior." Physics of Fluids A: Fluid Dynamics 3, no. 9 (September 1991): 2247–54. http://dx.doi.org/10.1063/1.857905.

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25

Lynch, David T. "Chaotic behavior of reaction systems: parallel cubic autocatalators." Chemical Engineering Science 47, no. 2 (February 1992): 347–55. http://dx.doi.org/10.1016/0009-2509(92)80025-8.

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26

Wu, Yuan-Long, Cheng-Hsiung Yang, and Chang-Hsi Wu. "Design of Initial Value Control for Modified Lorenz-Stenflo System." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/8424139.

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For the sake of complexity, unpredictability, and exceeding sensitivity to initial conditions in the chaotic systems, there were many studies for information encryption of chaotic systems in recent years. Enhancing the security in information encryption of chaotic systems, an initial value control circuit for chaotic systems is proposed in this paper. By way of changing the initial value, we can change the behavior of chaotic systems and also change the key of information encryption. An analog circuit is implemented to verify the initial value control circuit design.

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Anees, Amir, and Iqtadar Hussain. "A Novel Method to Identify Initial Values of Chaotic Maps in Cybersecurity." Symmetry 11, no. 2 (January 27, 2019): 140. http://dx.doi.org/10.3390/sym11020140.

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Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks and have been used as a source of diffusion in cybersecurity for more than two decades. With the addition of chaos, the overall strength of communication security systems can be increased, as seen in recent proposals. However, there is a major drawback of using chaos in communication security systems. Chaotic communication security systems rely on private keys, which are the initial values and parameters of chaotic systems. This paper shows that these chaotic communication security systems can be broken by identifying those initial values through the statistical analysis of standard deviation and variance. The proposed analyses are done on the chaotic sequences of Lorenz chaotic system and Logistic chaotic map and show that the initial values and parameters, which serve as security keys, can be retrieved and broken in short computer times. Furthermore, the proposed model of identifying the initial values can also be applied on other chaotic maps as well.

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Delgado-Aranda, F., I. Campos-Cantón, E. Tristán-Hernández, and P. Salas-Castro. "Hidden attractors from the switching linear systems." Revista Mexicana de Física 66, no. 5 Sept-Oct (September 1, 2020): 683. http://dx.doi.org/10.31349/revmexfis.66.683.

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Recently, chaotic behavior has been studied in dynamical systems that generates hidden attractors. Most of these systems have quadratic nonlinearities. This paper introduces a new methodology to develop a family of three-dimensional hidden attractors from the switching of linear systems. This methodology allows to obtain strange attractors with only one stable equilibrium, attractors with an infinite number of equilibria or attractors without equilibrium. The main matrix and the augmented matrix of every linear system are considered in Rouché-Frobenius theorem to analyze the equilibrium of the switching systems. Also, a systematic search assisted by a computer is used to find the chaotic behavior. Basic chaotic properties of the attractors are verified by the Lyapunov exponents.

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Castro, Jose, and Joaquin Alvarez. "Melnikov-Type Chaos of Planar Systems with Two Discontinuities." International Journal of Bifurcation and Chaos 25, no. 02 (February 2015): 1550027. http://dx.doi.org/10.1142/s0218127415500273.

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In this paper, the chaotic behavior of a driven planar system with two discontinuous terms and a pseudo-equilibrium point in the intersection of the discontinuity surfaces is analyzed. This scenario is not covered by smooth techniques of chaos analysis or other techniques like the extension of Melnikov's method for nonsmooth systems. In consequence, we propose to use an approximate model of the discontinuous system for which this technique can be applied, and compare the responses of both systems, the discontinuous and the approximate, when this last model is close, in a certain way, to the discontinuous system. One of the discontinuous terms, given by a sign function, is approximated by a saturation with high slope at the equilibrium point. Some conditions that determine the chaotic behavior of the approximate system are formally established, and the convergence of its chaotic orbits to some orbits of the discontinuous system, when the slope of the approximation is large enough, is shown. In particular, we show the similarity of the dynamical behavior of both systems where a chaotic behavior can be displayed, for a parameter region determined by the application of the Melnikov technique to nonsmooth systems. A comparison of the Feigenbaum diagrams, for a parameter range obtained from the application of this technique, shows the similarity of their dynamics and the chaotic nature of the discontinuous system.

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LU, HONGTAO, and WALLACE K. S. TANG. "CHAOTIC PHASE SHIFT KEYING IN DELAYED CHAOTIC ANTICONTROL SYSTEMS." International Journal of Bifurcation and Chaos 12, no. 05 (May 2002): 1017–28. http://dx.doi.org/10.1142/s0218127402004887.

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Based on the delayed feedback chaotic anticontrol systems, a new chaotic phase shift keying (CPSK) scheme is proposed for secure communications in this paper. The chaotic transmitter is a linear system with nonlinear delayed feedback in which a trigonometric function cos(·) is used. Such system can exhibit rich chaotic behavior with the choice of appropriate parameters. For an M-ary communication system where M=2n, each of these M possible symbols (n-bits) is firstly mapped to 2(m-1)π/M (with m=1, 2, …, M) which is used as the phase argument for the cos(·) function in the nonlinear feedback. Two different kinds of signals can be transmitted. In the first one, an appropriate linear combination of state variables is chosen as the transmitting signal based on the observer theory. In another one, a nonlinear component in the transmitter state equation is chosen. In both schemes, only a scalar chaotic signal is transmitted through the channel. Demodulation is based on the synchronization of the transmitter and the receiver, and different decoded phases correspond to different information signals.

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Clemente-López, Daniel, Esteban Tlelo-Cuautle, Luis-Gerardo de la Fraga, José de Jesús Rangel-Magdaleno, and Jesus Manuel Munoz-Pacheco. "Poincaré maps for detecting chaos in fractional-order systems with hidden attractors for its Kaplan-Yorke dimension optimization." AIMS Mathematics 7, no. 4 (2022): 5871–94. http://dx.doi.org/10.3934/math.2022326.

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<abstract><p>The optimization of fractional-order (FO) chaotic systems is challenging when simulating a considerable number of cases for long times, where the primary problem is verifying if the given parameter values will generate chaotic behavior. In this manner, we introduce a methodology for detecting chaotic behavior in FO systems through the analysis of Poincaré maps. The optimization process is performed applying differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms for maximizing the Kaplan-Yorke dimension ($ D_{KY} $) of two case studies: a 3D and a 4D FO chaotic systems with hidden attractors. These FO chaotic systems are solved applying the Grünwald-Letnikov method, and the Numba just-in-time (jit) compiler is used to improve the optimization process's time execution in Python programming language. The optimization results show that the proposed method efficiently optimizes FO chaotic systems with hidden attractors while saving execution time.</p></abstract>

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El Guezar, Fatima, and Hassane Bouzahir. "Chaotic Behavior in a Switched Dynamical System." Modelling and Simulation in Engineering 2008 (2008): 1–6. http://dx.doi.org/10.1155/2008/798395.

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We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator) which is a Scilab (scientific laboratory) package. The followed approach takes into account the hybrid nature of the circuit.

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SEIMENIS, J. "A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR." Modern Physics Letters B 03, no. 15 (October 1989): 1185–88. http://dx.doi.org/10.1142/s0217984989001813.

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We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

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BARRIO, ROBERTO, FERNANDO BLESA, and SERGIO SERRANO. "BEHAVIOR PATTERNS IN MULTIPARAMETRIC DYNAMICAL SYSTEMS: LORENZ MODEL." International Journal of Bifurcation and Chaos 22, no. 06 (June 2012): 1230019. http://dx.doi.org/10.1142/s0218127412300194.

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In experimental and theoretical studies of Dynamical Systems, there are usually several parameters that govern the models. Thus, a detailed study of the global parametric phase space is not easy and normally unachievable. In this paper, we show that a careful selection of one straight line (or other 1D manifold) permits us to obtain a global idea of the evolution of the system in some circumstances. We illustrate this fact with the paradigmatic example of the Lorenz model, based on a global study, changing all three parameters. Besides, searching in other regions, for all the detected behavior patterns in one straight line, we have been able to see that missing topological structures of the chaotic attractors may be found on the chaotic-saddles.

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Luo, Wenguang, Yingyuan Yu, Guangming Xie, and Hongli Lan. "Chaotic behavior analysis for a type of switched systems and its chaotic control." JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING 30, no. 3 (November 27, 2013): 235–41. http://dx.doi.org/10.3724/sp.j.1249.2013.03235.

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Yan, Wenhao, Zijing Jiang, Xin Huang, and Qun Ding. "A Three-Dimensional Infinite Collapse Map with Image Encryption." Entropy 23, no. 9 (September 17, 2021): 1221. http://dx.doi.org/10.3390/e23091221.

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Chaos is considered as a natural candidate for encryption systems owing to its sensitivity to initial values and unpredictability of its orbit. However, some encryption schemes based on low-dimensional chaotic systems exhibit various security defects due to their relatively simple dynamic characteristics. In order to enhance the dynamic behaviors of chaotic maps, a novel 3D infinite collapse map (3D-ICM) is proposed, and the performance of the chaotic system is analyzed from three aspects: a phase diagram, the Lyapunov exponent, and Sample Entropy. The results show that the chaotic system has complex chaotic behavior and high complexity. Furthermore, an image encryption scheme based on 3D-ICM is presented, whose security analysis indicates that the proposed image encryption scheme can resist violent attacks, correlation analysis, and differential attacks, so it has a higher security level.

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Tarokh, Mohammad Jafar, and Sina Golara. "Analyzing the Lead Time and Shipping Lot-Size in a Chaotic Supply Network." International Journal of Applied Logistics 2, no. 4 (October 2011): 15–28. http://dx.doi.org/10.4018/jal.2011100102.

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Supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. Supply networks are highly complex systems. The oscillations in demand and inventory as orders pass through the system have been widely studied in literature. Studies have shown that supply networks can display some of the key characteristics of chaotic systems. Chaos theory is the study of complex, nonlinear, dynamic systems; therefore it can be useful for studying the dynamics of supply networks. In this paper the authors implemented a system dynamic approach and simulated a chaotic multi-level supply network. The authors analyzed the effects of decision parameters, delivery lead time and shipping lot-size on chaotic behavior of the whole supply network. The simulation revealed that an increment in lead times or shipping lot-size has a similar impact on chaotic behavior of the system and reduces the chance of chaotic behavior occurrence.

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Bahrami, Amir, and Majid Tayarani. "Chaotic Behavior of Duffing Energy Harvester." Energy Harvesting and Systems 5, no. 3-4 (November 27, 2018): 67–71. http://dx.doi.org/10.1515/ehs-2018-0011.

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Abstract A wide bandwidth energy harvester is designed with the purpose of operation under multiple excitations, where the excitation frequencies are generally incommensurate and probably spectrally close to each other. Owing this wideness of bandwidth to the nonlinearity of the circuit escalates the jeopardy of chaotic behavior while the circuit is exposed to multiple energy sources. In this study, the recently introduced Duffing based energy harvester is analyzed under multiple excitations and finally, a safe margin is calculated to avoid tumultuous behaviors which may affect adjacent sensitive electrical systems. The mathematical analyses given in this paper can be generalized to other types of nonlinear resonators.

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PHAM, VIET-THANH, ARTURO BUSCARINO, LUIGI FORTUNA, and MATTIA FRASCA. "SIMPLE MEMRISTIVE TIME-DELAY CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 23, no. 04 (April 2013): 1350073. http://dx.doi.org/10.1142/s0218127413500739.

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Memristive systems have appeared in various application fields from nonvolatile memory devices and biological structures to chaotic circuits. In this paper, we propose two nonlinear circuits based on memristive systems in the presence of delay, i.e. memristive systems in which the state of the memristor depends on the time-delay. Both systems can exhibit chaotic behavior and, notably, in the second model, only a capacitor and a memristor are required to obtain chaos.

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Wang, Meibo, and Shaojuan Ma. "Hamilton Energy Control for the Chaotic System with Hidden Attractors." Complexity 2021 (August 4, 2021): 1–10. http://dx.doi.org/10.1155/2021/5530557.

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In this paper, the dynamic behavior and control of chaotic systems with hidden attractors are studied. Firstly, a class of autonomous chaotic systems without the equilibrium point is proposed. Secondly, quantitative analysis methods are applied to explore the dynamic behavior of the new chaotic systems. Then, the Hamilton energy function of the new system is calculated by the Helmholtz theorem and the energy feedback controller is designed. Finally, the effectiveness of the controller is verified by numerical simulations. Compared with the line feedback control, the control effect of Hamilton energy control is better.

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Ma, Da-Zhu, Zhi-Chao Long, and Yu Zhu. "Application of Indicators for Chaos in Chaotic Circuit Systems." International Journal of Bifurcation and Chaos 26, no. 11 (October 2016): 1650182. http://dx.doi.org/10.1142/s0218127416501820.

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Lyapunov exponent (LE), fast Lyapunov indicator (FLI), relative finite-time Lyapunov indicator (RLI), smaller alignment index (SALI), and generalized alignment index (GALI) are some of the available methods in most conservative systems. This study focuses on the effects of the above indicators on dissipative chaotic circuit systems such as the Lorenz system and a hyperchaotic model. Numerical experiments show that the performances of the chaos indicators in the hyperchaotic system are almost similar to those in the Lorenz system. These indicators clearly provide transition from chaotic to regular motion. However, FLI, RLI, SALI, and GALI cannot describe transition from chaos to hyperchaos. These indicators are also applied to study a new four-dimensional chaotic circuit system. The basic dynamic behaviors and structures are investigated analytically and numerically. The dynamic qualitative properties of individual orbits are observed using an oscilloscope. Moreover, the entire set of LE about the parameter is found to have three threshold values. Comparisons show that all chaos indicators are able to capture chaotic and periodic motion in chaotic circuit systems, but SALI displays significantly different behavior in several periodic orbits. SALI drops exponentially to zero for “morphologically regular” orbits that are actually unstable and sensitive to perturbation. This conclusion can also be confirmed by GALI.

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Ablay, Günyaz. "New 4D and 3D models of chaotic systems developed from the dynamic behavior of nuclear reactors." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 11 (November 2022): 113108. http://dx.doi.org/10.1063/5.0090518.

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The complex, highly nonlinear dynamic behavior of nuclear reactors can be captured qualitatively by novel four-dimensional (that is, fourth order) and three-dimensional (that is, third order) models of chaotic systems and analyzed with Lyapunov spectra, bifurcation diagrams, and phase diagrams. The chaotic systems exhibit a rich variety of bifurcation phenomena, including the periodic-doubling route to chaos, reverse bifurcations, anti-monotonicity, and merging chaos. The offset boosting method, which relocates the attractor’s basin of attraction in any direction, is demonstrated in these chaotic systems. Both constant parameters and periodic functions are seen in offset boosting phenomena, yielding chaotic attractors with controlled mean values and coexisting attractors.

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Hacinliyan, A. "Chaotic Behaviour in Dynamical Systems." Europhysics News 21, no. 1 (1990): 7–10. http://dx.doi.org/10.1051/epn/19902101007.

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44

WANG, XING-YUAN, GUO-BIN ZHAO, and YU-HONG YANG. "DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS." International Journal of Modern Physics B 27, no. 11 (April 25, 2013): 1350034. http://dx.doi.org/10.1142/s0217979213500343.

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This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

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Kopp, M., and A. Kopp. "A New 8D Lorenz-like Hyperchaotic System: Computer Modelling, Circuit Design and Arduino Uno Board Implementation." Journal of Telecommunication, Electronic and Computer Engineering (JTEC) 15, no. 2 (June 30, 2023): 37–46. http://dx.doi.org/10.54554/jtec.2023.15.02.005.

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This paper presents the construction of Matlab-Simulink and LabView models for a novel nonlinear dynamic system of equations in an eight-dimensional (8D) phase space. The Lyapunov exponent spectrum and Kaplan-York dimension were calculated with fixed parameters of the 8D dynamical system. The presence of two positive Lyapunov exponents indicates hyperchaotic behavior. The fractional Kaplan-York dimension shows the fractal structure of strange attractors. An adaptive controller was used to stabilize the 8D chaotic system with unknown system parameters, and an active control method was derived to achieve global chaotic synchronization of two identical 8D chaotic systems with unknown system parameters. Using the results from Matlab-Simulink and LabView models, a chaotic signal generator for the 8D chaotic system was implemented in the Multisim environment. The simulation results of chaotic behavior in the Multisim environment demonstrate similar behavior compared to simulation results from Matlab-Simulink and LabView models. To visualize the new 8D chaotic system, we employed an Arduino Uno board along with eight light-emitting diodes (LEDs). Furthermore, we demonstrated the capability to simulate the new 8D chaotic system in the Proteus 8 environment using the Arduino Uno microcontroller. This advancement in the understanding and implementation of chaotic systems opens doors to numerous possibilities in the realm of secure communication and control systems.

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Nuñez-Perez, Jose-Cruz, Vincent-Ademola Adeyemi, Yuma Sandoval-Ibarra, Francisco-Javier Perez-Pinal, and Esteban Tlelo-Cuautle. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms." Mathematics 9, no. 11 (May 25, 2021): 1194. http://dx.doi.org/10.3390/math9111194.

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This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

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Arshad, Muhammad Haseeb, Mahmoud Kassas, Alaa E. Hussein, and Mohammad A. Abido. "A Simple Technique for Studying Chaos Using Jerk Equation with Discrete Time Sine Map." Applied Sciences 11, no. 1 (January 4, 2021): 437. http://dx.doi.org/10.3390/app11010437.

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Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system’s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent. Experimental verification of the system was carried out using Op-Amps with analog multipliers.

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MacCluer, C. R. "Chaos in Linear Distributed Systems." Journal of Dynamic Systems, Measurement, and Control 114, no. 2 (June 1, 1992): 322–24. http://dx.doi.org/10.1115/1.2896532.

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49

Zhang, Pei, Renyu Yang, Renhuan Yang, Gong Ren, Xiuzeng Yang, Chuangbiao Xu, Baoguo Xu, Huatao Zhang, Yanning Cai, and Yaosheng Lu. "Parameter estimation for fractional-order chaotic systems by improved bird swarm optimization algorithm." International Journal of Modern Physics C 30, no. 11 (November 2019): 1950086. http://dx.doi.org/10.1142/s0129183119500864.

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The essence of parameter estimation for fractional-order chaotic systems is a multi-dimensional parameter optimization problem, which is of great significance for implementing fractional-order chaos control and synchronization. Aiming at the parameter estimation problem of fractional-order chaotic systems, an improved algorithm based on bird swarm algorithm is proposed. The proposed algorithm further studies the social behavior of the original bird swarm algorithm and optimizes the foraging behavior in the original bird swarm algorithm. This method is applied to parameter estimation of fractional-order chaotic systems. Fractional-order unified chaotic system and fractional-order Lorenz system are selected as two examples for parameter estimation systems. Numerical simulation shows that the algorithm has better convergence accuracy, convergence speed and universality than bird swarm algorithm, artificial bee colony algorithm, particle swarm optimization and genetic algorithm.

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BERAN, ZDENĚK, and SERGEJ ČELIKOVSÝ. "GENERALIZED SEMIFLOWS AND CHAOS IN MULTIVALUED DYNAMICAL SYSTEMS." International Journal of Modern Physics B 26, no. 25 (September 10, 2012): 1246016. http://dx.doi.org/10.1142/s0217979212460162.

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This contribution addresses a possible description of the chaotic behavior in multivalued dynamical systems. For the multivalued system formulated via differential inclusion the practical conditions on the right-hand side are derived to guarantee existence of a solution, which leads to the chaotic behavior. Our approach uses the notion of the generalized semiflow but it does not require construction of a selector on the set of solutions. Several applications are provided by concrete examples of multivalued dynamical systems including the one having a clear physical motivation.

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