Optimizing the positive Lyapunov exponent in multi-scroll chaotic oscillators with differential evolution algorithm

• Published in: Applied mathematics and computation Vol. 219; no. 15; pp. 8163 - 8168
• Main Authors: Carbajal-Gomez, V H, Tlelo-Cuautle, E, Fernandez, F V
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2013
• Subjects: Algorithms; Bifurcation diagram; Bifurcations; Chaos theory; Chaotic oscillator; Differential evolution; Evolution; Lyapunov exponent; Lyapunov exponents; Mathematical analysis; Mathematical models; Multi-scrolls; Oscillators; Differential evolution; Bifurcation diagram; Multi-scrolls; Chaotic oscillator; Lyapunov exponent
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2013.01.072

We introduce the application of the differential evolution algorithm (DE) to optimize the positive Lyapunov exponent in a multi-scroll chaotic oscillator based on saturated nonlinear function series. The positive Lyapunov exponent is optimized from two to nine scrolls by sweeping the coefficients of the chaotic oscillator. In this article, the case of study has four coefficients, so that the feasible solutions for a,b,c, and d1, are used to generate the bifurcation diagrams for the cases from two to nine scrolls taking c as the bifurcation parameter to demonstrate that high values of the positive Lyapunov exponent can be guaranteed when a,b,d1 take values higher than 0.7, while c takes values lower than 0.3.