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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 851970, 11 pages
Research Article

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

Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, 72570 Puebla, PUE, Mexico

Received 25 July 2013; Accepted 21 October 2013

Academic Editor: Andrei Korobeinikov

Copyright © 2013 Jesus Manuel Munoz-Pacheco et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.