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

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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 regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from -piecewise linear variational equations and their associated -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 -PWL Variational Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, December.
    • Handle: RePEc:hin:jnlaaa:851970
    DOI: 10.1155/2013/851970
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