On the Relation between the Number of Scrolls and the Lyapunov Exponents in PWL-functions-based n-Scroll Chaotic Oscillators

Abstract

A challenge in the physical design of n-scroll attractors is to generate a large number of scrolls. However, an open question is: Does the large number of scrolls determine a better chaotic behavior? We present a partial answer to this question by computing the Lyapunov exponents for piecewise-linear (PWL) functions based on n-scroll third order chaotic oscillators, namely: Zhong modified Chua's circuit, Yu modified Chua's circuit, saturated function series based chaotic oscillator, and generalized Chua's circuit with saw-tooth function. Three different integration methods (forward Euler, fourth order Runge Kutta and Matlab (c) ODE 45) are used in order to show that the positive Lyapunov exponent is not significantly incremented in relation with the number of scrolls.