Determining the Control Parameters Value of Nonlinear Dynamical Systems for Generating Chaos

Abstract

This paper proposes a numerical method for determining the control parameter value of nonlinear dynamical systems such that they get chaotic. It can reduce the burden of a person who needs to generate chaos from them. The proposed method combines (a) an efficient numerical method for approximating the maximal Lyapunov exponent with sufficient accuracy, and (b) Particle Swarm Optimization (PSO) method for maximizing the maximum Lyapunov exponent numerically. In addition, (c) the boundedness of trajectory is also introduced as a constraint. Empirical results will also be presented, which verify the usefulness of the proposed method.