Solving Problems in Chaos Control though an Differential Evolution Algorithm with Region Zooming

Abstract

In this paper, a novel scheme is propose to solve the problems in chaos control via a nonnegative multi–modal nonlinear optimization, which finds the unstable periodic orbits and best parameters of chaos system such that the objective function is minimized. The novel scheme embeds with a differential evolution algorithm consisting of techniques in three aspects: uniform design to the initial population, deflection and stretching to the objective functions, and the region zooming self–adaptively, which result in a much more effective searching mechanism with fine equilibrium between exploitation and exploration. To exhibit the new scheme’s performance, the experiments done to Hénon, Chen and Lü system are given, and the simulations done show that the method has better adaptability, dependability and robustness.