On maximizing positive Lyapunov exponents in a chaotic oscillator with heuristics

Abstract

A positive Lyapunov exponent indicates the presence of chaos in a dynamical system. In this manner, computing its maximum value guarantees the unpredictability grade of a chaotic system. In this investigation we present the application and comparison of two heuristics: Differential Evolution (DE) and Particle Swarm Optimization (PSO), to maximize the positive Lyapunov exponent in a multi-scroll chaotic oscillator based on saturated nonlinear function series. The computed results show that DE and PSO algorithms are suitable to maximize the positive Lyapunov exponent of truncated coefficients over the continuous spaces. In addition, the phase diagrams show that for a small positive Lyapunov exponent the attractors are well defined, while for its maximum value, the attractors are not well appreciated because the unpredictability grade of the chaotic oscillator is increased.