A novel non-Lyapunov approach in discrete chaos system with rational fraction control by artificial bee colony algorithm

This paper is concerned with a novel chaos control approach for discrete chaotic systems with rational fraction. An artificial bee colony (ABC) algorithm is newly introduced to solve this problem in a non-Lyapunov way. The approach realize the following three steps by ABC: detecting chaos system´s dynamical behaviors such as extreme values and unstable periodic points; directing the system to its unstable fix point from any initial point by global controlling factors; stabilizing the system on its unstable fix point with a multi-model control. The details of applying the proposed method are given and the illustrative experiments done to a discrete chaos system with rational fraction show the proposed strategy is effective and robust.