Determining the Lyapunov spectrum of continuous-time 1D and 2D multiscroll chaotic oscillators via the solution of \(m\)-PWL variational equations. (English) Zbl 1470.34125

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

Abstr. Appl. Anal. 2013, Article ID 851970, 11 p. (2013).

Summary: 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.

MSC:

34C28	Complex behavior and chaotic systems of ordinary differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

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