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Doctoral Thesis
DOI
10.11606/T.43.2001.tde-04122013-105609
Document
Author
Full name
Elinei Pinto dos Santos
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2001
Supervisor
Committee
Caldas, Ibere Luiz (President)
Grebogi, Celso
Macau, Elbert Einstein Nehrer
Sartorelli, Jose Carlos
Viana, Ricardo Luiz
Title in Portuguese
Bifurcações, controle e sincronização do caos nos circuitos de Matsumoto-Chua
Keywords in Portuguese
Bifurcações
Caos
Controle
Sincronização
Abstract in Portuguese
Neste trabalho utilizamos técnicas de controle e sincronização de sistemas caóticos, visando o uso delas para comunicação com caos. Aplicamos tais técnicas no circuito elétrico de Matsumoto-Chua. Inicialmente, mostramos a sensibilidade dos atratores deste circuito quando variamos os seus parâmetros. Determinamos as suas bacias de atração. Através da análise biespectral, verificamos que o acoplamento quadrático é alto para o atrator tipo Rössler, e quase nulo para o atrator Espiral-Dupla. Para a caracterização global do circuito, apresentamos diagramas, no espaço de parâmetros, com os valores dos expoentes de Lyapunov ou autocorrelação. A seguir estudamos esse circuito com uma perturbação senoidal. Com isto, identificamos novos cenários para a transição para o caos a partir da quase periodicidade. Duas destas transições foram identificados pela primeira vez nesse circuito. Aplicamos ao circuito cinco métodos de controle de caos: supressão de caos por sincronização de freqüências, controle de órbitas periódicas instáveis pelos métodos OGY e de realitnentação , estabilização no ponto ele equilíbrio (método de Hwang), migração e arraste (método OPCL). Finalmente, consideramos dois circuitos de Matsumo-Chua acoplados e determinamos as suas bacias de sincronização. Mostramos que a sincronização dos circuitos acoplados pode não depender das condições iniciais (fronteira das bacias contínua) ou ser extremamente sensível às condições iniciais (fronteira elas bacias elo tipo crivada ou intercrivada).
Title in English
Bifurcations, Control and Synchronization of Chaos in Matsumoto-Chua Circuits
Keywords in English
Bifurcations
Chaos
Control
Synchronization
Abstract in English
In this work we use control and synchronization of chaos techniques aiming their implementation in communicating with chaos. These techniques are applied into the electric circuit of Matsumoto-Chua. Initialty, we show the sensibility of the attractors under parameter variations. We determine the attractor basin of attractions. Through the bi-spectral analysis, we verify that the quadratic coupling is high for the Rössler-type attractor, and almost null for the Double-Scroll attractor. For the global charactcrization of this system, we show parameter diagrams of the Lyapunov exponents or auto-correlation. We also study this circuit under a sinusoidal perturbation. In this configuration, we identify new scenario for the transition to chaos through quasi-periodicity. Two of these transitions are identified by us for the first time in this perturbed circuit. We apply five control of chaos techniques: chaos suppression by frequency synchronization, control of unstable periodic orbits by the OGY and feed-back methods, stabilization of the equilibrium points (Hwang method), migration and entrainment (OPCL method). Finally, we consider two acoupled Matsumoto-Chua's circuits and determine their synchronization basins. We show that the synchronization in these coupled circuits may not depend on the initial conditions (continuous synchronization basin boundary) or may depend extremely on the initial conditions (riddled or intermingled synchronization basin boundaries).
 
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RE33281Santos.pdf (9.23 Mbytes)
Publishing Date
2014-02-21
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • SANTOS, E. P., BAPTISTA, M. S., and CALDAS, I. L. Dealing with final state sensitivity for synchronous communication. Physica. A , 2002, vol. 308, p. 101-112.
  • SANTOS, E. P., BAPTISTA, M. S., and Caldas, I L. Control and Migration in The Matsumoto-Chua Circuit. In Nonlinear Dynamics, Chaos, Control, and Their Applications to Engineering Sciences, Campos do Jordão, 2002. Proc. Nonlinear Dynamics, Chaos, Control, and Their Applications to Engineering Sciences.Rio Claro : Brazilian Society of Mechanical Sciences and American Academy of Mechanics, 2002.
  • SANTOS, E. P., Caldas, I L, and BAPTISTA, M. S. Two-Frequency Torus Breakdowon in the Driven Matsumoto-Chua Electronic Circuit. In Nonlinear Dynamics, Chaos, Control, and Their Applications to Engineering Sciences, Campos do Jordão, 2002. Proc. Nonlinear Dynamics, Chaos, Control, and Their Applications to Engineering Sciences.Rio Claro : Brazilian Society of Mechanical Sciences and American Academy of Mechanics, 2002.
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