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Relevant bibliographies by topics / Wavelets (Mathematics) Chaotic behavior in systems

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Academic literature on the topic 'Wavelets (Mathematics) Chaotic behavior in systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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Journal articles on the topic "Wavelets (Mathematics) Chaotic behavior in systems"

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CAMPOS-CANTÓN, E., J. S. MURGUÍA, and H. C. ROSU. "CHAOTIC DYNAMICS OF A NONLINEAR ELECTRONIC CONVERTER." International Journal of Bifurcation and Chaos 18, no. 10 (2008): 2981–3000. http://dx.doi.org/10.1142/s0218127408022202.

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The nonlinear electronic converter used by Rulkov and collaborators [Rulkov et al., 2001], which is the core of their chaotic oscillator, is modeled and simulated numerically by means of an appropriate direct relationship between the experimental values of the electronic components of the system and the mathematical model. This relationship allows us to analyze the chaotic behavior of the model in terms of a particular bifurcation parameter k. Varying the parameter k, quantitative results of the dynamics of the numerical system are presented, which are found to be in good agreement with the experimental measurements that we performed as well. Moreover, we show that this nonlinear converter belongs to a class of 3-D systems that can be mapped to the unfolded Chua's circuit. We also report a wavelet transform analysis of the experimental and numerical chaotic time series data of this chaotic system. The wavelet analysis provides us with information on such systems in terms of the concentration of energy which is the standard electromagnetic interpretation of the L2 norm of a given signal.

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AHALPARA, DILIP P., and JITENDRA C. PARIKH. "MODELING TIME SERIES DATA OF REAL SYSTEMS." International Journal of Modern Physics C 18, no. 02 (2007): 235–52. http://dx.doi.org/10.1142/s0129183107010474.

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Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis and a prediction method proposed by Lorenz is applied to make out of sample predictions at different regions of the time series. The prediction capability of this method is studied by considering several improvements over this method. We then apply this approach to a real financial time series. The smooth time series is modeled using techniques of non linear dynamics. Our results for predictions suggest that the modified Lorenz method gives better predictions compared to those from the original Lorenz method. Fluctuations are analyzed using probabilistic considerations.

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AL-ASSAF, YOUSEF, and WAJDI M. AHMAD. "PARAMETER IDENTIFICATION OF CHAOTIC SYSTEMS USING WAVELETS AND NEURAL NETWORKS." International Journal of Bifurcation and Chaos 14, no. 04 (2004): 1467–76. http://dx.doi.org/10.1142/s0218127404009910.

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This paper addresses the problem of reconstructing a slowly-varying information-bearing signal from a parametrically modulated, nonstationary dynamical signal. A chaotic electronic oscillator model characterized by one control parameter and a double-scroll-like attractor is used throughout the study. Wavelet transforms are used to extract features of the chaotic signal resulting from parametric modulation of the control parameter by the useful signal. The vector of feature coefficients is fed into a feed-forward neural network that recovers the embedded information-bearing signal. The performance of the developed method is cross-validated through reconstruction of randomly-generated control parameter patterns. This method is applied to the reconstruction of speech signals, thus demonstrating its potential utility for secure communication applications. Our results are validated via numerical simulations.

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Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Intermittent transition to chaos in vibroimpact system." Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 475–86. http://dx.doi.org/10.2478/amns.2018.2.00037.

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AbstractChaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.

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NAKAO, HIROYA, TSUYOSHI MISHIRO, and MICHIO YAMADA. "VISUALIZATION OF CORRELATION CASCADE IN SPATIOTEMPORAL CHAOS USING WAVELETS." International Journal of Bifurcation and Chaos 11, no. 05 (2001): 1483–93. http://dx.doi.org/10.1142/s0218127401002833.

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We propose a simple method to visualize spatiotemporal correlation between scales using wavelets, and apply it to two typical spatiotemporally chaotic systems, namely to coupled complex Ginzburg–Landau oscillators with diffusive interaction, and those with nonlocal interaction. Reflecting the difference between underlying dynamical processes, our method provides distinctive results for those two systems. Especially, for the nonlocally interacting case where the system exhibits fractal amplitude patterns and power-law spectrum, it clearly visualizes the dynamical cascade process of spatiotemporal correlation between scales.

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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 (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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Allingham, David, Matthew West, and Alistair I. Mees. "Wavelet Reconstruction of Nonlinear Dynamics." International Journal of Bifurcation and Chaos 08, no. 11 (1998): 2191–201. http://dx.doi.org/10.1142/s0218127498001789.

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We investigate the reconstruction of embedded time-series from chaotic dynamical systems using wavelets. The standard wavelet transforms are not applicable because of the embedding, and we use a basis pursuit method which on its own does not perform very well. When this is combined with a continuous optimizer, however, we obtain very good models. We discuss the success of this method and apply it to some data from a vibrating string experiment.

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AWREJCEWICZ, J., A. V. KRYSKO, and V. SOLDATOV. "ON THE WAVELET TRANSFORM APPLICATION TO A STUDY OF CHAOTIC VIBRATIONS OF THE INFINITE LENGTH FLEXIBLE PANELS DRIVEN LONGITUDINALLY." International Journal of Bifurcation and Chaos 19, no. 10 (2009): 3347–71. http://dx.doi.org/10.1142/s0218127409024803.

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Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the Bubnov–Galerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.

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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 (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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Mukhamedov, F. "On the chaotic behavior of cubic p-adic dynamical systems." Mathematical Notes 83, no. 3-4 (2008): 428–31. http://dx.doi.org/10.1134/s0001434608030139.

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Dissertations / Theses on the topic "Wavelets (Mathematics) Chaotic behavior in systems"

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Constantine, William L. B. "Wavelet techniques for chaotic and fractal dynamics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/7124.

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Ghosh, Dastidar Samanwoy. "Models of EEG data mining and classification in temporal lobe epilepsy: wavelet-chaos-neural network methodology and spiking neural networks." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180459585.

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Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

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The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the concept of bi-shadowing in a Banach space is defined and proved for semi-hyperbolic dynamical systems generated by Lipschitz mappings. As an application to the concept of bishadowing, linear delay differential equations are shown to be bi-shadowing with respect to pseudo-trajectories generated by nonlinear small perturbations of the linear delay equation. This shows robustness of solutions of the linear delay equation with respect to small nonlinear perturbations. Complicated dynamical behaviour is often a consequence of the expansivity of a dynamical system. Semi-hyperbolic dynamical systems generated by Lipschitz mappings on a Banach space are shown to be exponentially expansive, and explicit rates of expansion are determined. The result is applied to a nonsmooth noninvertible system generated by delay differential equation. It is shown that semi-hyperbolic mappings are locally φ-contracting, where -0 is the Hausdorff measure of noncompactness, and that a linear operator is semi-hyperbolic if and only if it is φ-contracting and has no spectral values on the unit circle. The definition of φ-bi-shadowing is given and it is shown that semi-hyperbolic mappings in Banach spaces are φ-bi-shadowing with respect to locally condensing continuous comparison mappings. The result is applied to linear delay differential equations of neutral type with nonsmooth perturbations. Finally, it is shown that a small delay perturbation of an ordinary differential equation with a homoclinic trajectory is chaotic.

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Huddlestone, Grant E. "Implementation and evaluation of two prediction techniques for the Lorenz time series." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53459.

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Thesis (MSc)-- Stellenbosch University, 2003.<br>ENGLISH ABSTRACT: This thesis implements and evaluates two prediction techniques used to forecast deterministic chaotic time series. For a large number of such techniques, the reconstruction of the phase space attractor associated with the time series is required. Embedding is presented as the means of reconstructing the attractor from limited data. Methods for obtaining the minimal embedding dimension and optimal time delay from the false neighbour heuristic and average mutual information method are discussed. The first prediction algorithm that is discussed is based on work by Sauer, which includes the implementation of the singular value decomposition on data obtained from the embedding of the time series being predicted. The second prediction algorithm is based on neural networks. A specific architecture, suited to the prediction of deterministic chaotic time series, namely the time dependent neural network architecture is discussed and implemented. Adaptations to the back propagation training algorithm for use with the time dependent neural networks are also presented. Both algorithms are evaluated by means of predictions made for the well-known Lorenz time series. Different embedding and algorithm-specific parameters are used to obtain predicted time series. Actual values corresponding to the predictions are obtained from Lorenz time series, which aid in evaluating the prediction accuracies. The predicted time series are evaluated in terms of two criteria, prediction accuracy and qualitative behavioural accuracy. Behavioural accuracy refers to the ability of the algorithm to simulate qualitative features of the time series being predicted. It is shown that for both algorithms the choice of the embedding dimension greater than the minimum embedding dimension, obtained from the false neighbour heuristic, produces greater prediction accuracy. For the neural network algorithm, values of the embedding dimension greater than the minimum embedding dimension satisfy the behavioural criterion adequately, as expected. Sauer's algorithm has the greatest behavioural accuracy for embedding dimensions smaller than the minimal embedding dimension. In terms of the time delay, it is shown that both algorithms have the greatest prediction accuracy for values of the time delay in a small interval around the optimal time delay. The neural network algorithm is shown to have the greatest behavioural accuracy for time delay close to the optimal time delay and Sauer's algorithm has the best behavioural accuracy for small values of the time delay. Matlab code is presented for both algorithms.<br>AFRIKAANSE OPSOMMING: In hierdie tesis word twee voorspellings-tegnieke geskik vir voorspelling van deterministiese chaotiese tydreekse ge"implementeer en geevalueer. Vir sulke tegnieke word die rekonstruksie van die aantrekker in fase-ruimte geassosieer met die tydreeks gewoonlik vereis. Inbedmetodes word aangebied as 'n manier om die aantrekker te rekonstrueer uit beperkte data. Metodes om die minimum inbed-dimensie te bereken uit gemiddelde wedersydse inligting sowel as die optimale tydsvertraging te bereken uit vals-buurpunt-heuristiek, word bespreek. Die eerste voorspellingsalgoritme wat bespreek word is gebaseer op 'n tegniek van Sauer. Hierdie algoritme maak gebruik van die implementering van singulierwaarde-ontbinding van die ingebedde tydreeks wat voorspel word. Die tweede voorspellingsalgoritme is gebaseer op neurale netwerke. 'n Spesifieke netwerkargitektuur geskik vir deterministiese chaotiese tydreekse, naamlik die tydafhanklike neurale netwerk argitektuur word bespreek en ge"implementeer. 'n Modifikasie van die terugprapagerende leer-algoritme vir gebruik met die tydafhanklike neurale netwerk word ook aangebied. Albei algoritmes word geevalueer deur voorspellings te maak vir die bekende Lorenz tydreeks. Verskeie inbed parameters en ander algoritme-spesifieke parameters word gebruik om die voorspelling te maak. Die werklike waardes vanuit die Lorentz tydreeks word gebruik om die voorspellings te evalueer en om voorspellingsakkuraatheid te bepaal. Die voorspelde tydreekse word geevalueer op grand van twee kriteria, naamlik voorspellingsakkuraatheid, en kwalitatiewe gedragsakkuraatheid. Gedragsakkuraatheid verwys na die vermoe van die algoritme om die kwalitatiewe eienskappe van die tydreeks korrek te simuleer. Daar word aangetoon dat vir beide algoritmes die keuse van inbed-dimensie grater as die minimum inbeddimensie soos bereken uit die vals-buurpunt-heuristiek, grater akkuraatheid gee. Vir die neurale netwerkalgoritme gee 'n inbed-dimensie grater as die minimum inbed-dimensie ook betel' gedragsakkuraatheid soos verwag. Vir Sauer se algoritme, egter, word betel' gedragsakkuraatheid gevind vir 'n inbed-dimensie kleiner as die minimale inbed-dimensie. In terme van tydsvertraging word dit aangetoon dat vir beide algoritmes die grootste voorspellingsakkuraatheid verkry word by tydvertragings in 'n interval rondom die optimale tydsvetraging. Daar word ook aangetoon dat die neurale netwerk-algoritme die beste gedragsakkuraatheid gee vir tydsvertragings naby aan die optimale tydsvertraging, terwyl Sauer se algoritme betel' gedragsakkuraatheid gee by kleineI' waardes van die tydsvertraging. Die Matlab kode van beide algoritmes word ook aangebied.

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Damacena, Thais Borges 1988. "A singularidade dobra-dobra e o caos não determinístico." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305969.

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Orientador: Marco Antonio Teixeira<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T09:21:57Z (GMT). No. of bitstreams: 1 Damacena_ThaisBorges_M.pdf: 1821590 bytes, checksum: 6b7242d4adbe1ac4b9b0dcbe04dd70b7 (MD5) Previous issue date: 2012<br>Resumo: Um campo vetorial descontínuo 3D sobre uma superfície suave de codimensão um, pode ser genericamente tangente a ambos os lados da superfície em um ponto p. Os pontos onde esse fenômeno ocorre são chamados de singularidade dobra-dobra. Nesse trabalho, estudamos a dinâmica local de um sistema dinâmico suave por partes tri-dimensional em uma dobra-dobra. Vimos que a dinâmica local depende principalmente de um único parâmetro que controla uma bifurcação. Especificamente no caso onde as dobras são ambas invisíveis, a chamada singularidade Teixeira, encontramos que o sistema pode admitir um fluxo exibindo dinâmica caótica, mas não determinística<br>Abstract: A 3D discontinuous vector field on a smooth surface of codimension one, can be generically tangent to both sides of the surface at a point p. The points where this phenomenon occurs are called two-fold singularities. In this project, we study the local dynamics of a three-dimensional piecewise smooth dynamical systems at a two-fold. We have seen that the local dynamics depends mainly on a single parameter that controls a bifurcation. Specifically in the case where the folds are both invisibles, the so-called singularity Teixeira, we find that the system can admit a flow exhibiting chaotic but non-deterministic dynamics<br>Mestrado<br>Matematica<br>Mestre em Matemática

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Monte, Brent M. "Chaos and the stock market." CSUSB ScholarWorks, 1994. https://scholarworks.lib.csusb.edu/etd-project/860.

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Hoffman, Lance Douglas. "The control of chaotic maps." Thesis, 2012. http://hdl.handle.net/10210/6845.

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2003<br>Some important ideas froni classical control theory are introduced with the intention of applying them to chaotic dynamical systems, in particular the coupled logistic equations. The structure of this dissertation is such that a strong foundation in control theory is first established before introducing the coupled logistic map or the methods of control and targetting in chaotic systems. In chapter 1 some aspects of classical control theory are reviewed. Continuous- and discrete-time dynamical systems are introduced and the existence and uniquendss criteria for the continuous case are explored via Lipschitz continuity. The matrix form of an inhomogeneous linear differential equation is presented and several properties of the associated transition matrix are discussed. Several linear algebraic ideas, most notably the Cayley-Hamilton theorem, are employed to explore the important concepts of controllability and observability in linear systems. The stabilisability problem is thoroughly investigated. Finally, the neighbourhood properties of continuous nonlinear dynamical systems with reference to controllability, stability and noise are established. Chapter 2 places emphasis on canonical forms, pole assignments and state observers. The decomposition of a general system into distinct components is facilitated by the general structure theorem, which is proved. The pole placement problem is described and the correspondence between the stabilisability of a system and the placement of poles is noted by the use'of a socalled feedback matrix. Lastly, the notion of a state observer, with reference to some dynamic feedback law, is introduced. The dynamics of the coupled logistic equations are studied in chapter 3. The fixed points of the map are calculated and the subsequent dynamical consequences explored. Using methods introduced in earlier chapters, the stability of the map is investigated. Using the so-called variational equations, the Lyapunov exponents are computed and used to classify, the motion of the system for the parameter values r and a. This chapter concludes with a discussion of the basins of attraction and critical curves associated with the coupled logistic equations. It is in chapter 4 that the models for controlling chaos are instantiated. The famous Ott-Grebogi- Yorke (OGY) method for controlling chaos is explained and related to the pole placement problem, discussed previously. The theory is extended to study the control of periodic orbits with periods greater than one.

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Nelson, Kevin Taylor Turner Jack S. Driebe Dean J. "Density evolution in systems with slow approach to equilibrium." 2004. http://repositories.lib.utexas.edu/bitstream/handle/2152/2141/nelsonkt042.pdf.

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Nelson, Kevin Taylor. "Density evolution in systems with slow approach to equilibrium." Thesis, 2004. http://hdl.handle.net/2152/2141.

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Archer, Kassie. "Box-counting dimension and beyond /." 2009. http://hdl.handle.net/10288/1259.

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Books on the topic "Wavelets (Mathematics) Chaotic behavior in systems"

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Xiaomo, Jiang, ed. Intelligent infrastructure: Neural networks, wavelets, and chaos theory for intelligent transportation systems and smart structures. CRC Press, 2008.

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Masaya, Yamaguchi. Mathematics of fractals. American Mathematical Society, 1997.

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An introduction to chaotic dynamical systems. 2nd ed. Addison-Wesley, 1989.

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An introduction to chaotic dynamical systems. Benjamin/Cummings, 1986.

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An introduction to chaotic dynamical systems. 2nd ed. Westview Press, 2003.

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Steeb, W. H. Chaotic and random motion. Rand Afrikaans Univiversity, 1987.

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Ian, Stewart. Does God play dice?: The mathematics of chaos. Basil Blackwell, 1990.

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Chen, Goong. Chaotic maps: Dynamics, fractals, and rapid fluctuations. Morgan & Claypool, 2011.

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Field, Mike. Symmetry in chaos: A search for pattern in mathematics, art and nature. Oxford University Press, 1995.

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1945-, Golubitsky Martin, ed. Symmetry in chaos: A search for pattern in mathematics, art, and nature. 2nd ed. Society for Industrial and Applied Mathematics, 2009.

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Book chapters on the topic "Wavelets (Mathematics) Chaotic behavior in systems"

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Martins, Ricardo M., and Durval J. Tonon. "The Chaotic Behavior of Piecewise Smooth Dynamical Systems on Torus and Sphere." In Trends in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55642-0_22.

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"NON-LINEAR AND CHAOTIC SYSTEMS." In The Mathematics of Behavior. Cambridge University Press, 2001. http://dx.doi.org/10.1017/cbo9780511618222.006.

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Conference papers on the topic "Wavelets (Mathematics) Chaotic behavior in systems"

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Iliuk, Itamar, José M. Balthazar, Angelo M. Tusset, Vinicius Piccirillo, Reyolando M. L. R. F. Brasil, and José R. C. Piqueira. "The Use of Wavelets Analysis to Characterize the Dynamic Behavior of Energy Transfer Vibrational Systems." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34266.

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This paper describes the use of wavelet analysis for identification of regular and irregular behavior of dynamical systems. We are focused in single and double-well potential energy harvesting systems that present either periodic or chaotic behavior. To identify the behavior of dynamical systems is of major importance in predicting possible energy harvesting from that system. Using Morlet wavelets, the oscillatory motions of a set of systems were identified with good accuracy. The visualization of the scalograms and global energy spectrum are very useful tools to validate the type of motion found, periodic, quasi-periodic or chaotic. Wavelet analysis can be used to find which amplitude and frequency of operation that generates more energy for each model. Wavelet analysis is a technique used as a tool to assist the validation of the presence of chaos in dynamic systems, together with well consolidated techniques as Lyapunov exponents and Poincare maps.

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