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Determining the Lyapunov Spectrum of Continuous‐Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of m‐PWL Variational Equations

Author

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  • Jesus Manuel Munoz-Pacheco
  • Luz del Carmen Gómez-Pavón
  • Olga Guadalupe Félix-Beltrán
  • Arnulfo Luis-Ramos

Abstract

An algorithm to compute the Lyapunov exponents of piecewise linear function‐based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m‐piecewise linear variational equations and their associated m‐Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp‐based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double‐scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Suggested Citation

  • Jesus Manuel Munoz-Pacheco & Luz del Carmen Gómez-Pavón & Olga Guadalupe Félix-Beltrán & Arnulfo Luis-Ramos, 2013. "Determining the Lyapunov Spectrum of Continuous‐Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of m‐PWL Variational Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:851970
    DOI: 10.1155/2013/851970
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    References listed on IDEAS

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    1. Yeong-Jeu Sun, 2012. "DII‐Based Linear Feedback Control Design for Practical Synchronization of Chaotic Systems with Uncertain Input Nonlinearity and Application to Secure Communication," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Zhang, Zhong & Chen, Guanrong, 2008. "Liquid mixing enhancement by chaotic perturbations in stirred tanks," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 144-149.
    3. Yeong-Jeu Sun, 2012. "DII-Based Linear Feedback Control Design for Practical Synchronization of Chaotic Systems with Uncertain Input Nonlinearity and Application to Secure Communication," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, December.
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