A novel artificial bee colony algorithm with space contraction for unknown parameters identification and time-delays of chaotic systems

This paper is concerned with the uncertain parameters and time-delay of nonlinear chaotic systems, which is of vital significance in chaos control and synchronization. In this article, a novel artificial bee colony algorithm (ABC), with space contraction and optimization technique based on the foraging behavior of honeybees, is newly proposed to solve the estimation problem via a nonnegative multi-modal nonlinear optimization, which finds a best combination of parameters such that an objective function is minimized. The illustrative examples, in Lorénz, Chen, Lü chaos systems and Mackey–Glass time-delay chaos system, are given though ABC and ABC with space contraction self-adaptively (ABCSC) respectively. Simulation are done and comparisons to some existing results by a recent version of ABC, HTCMIABC demonstrate that ABCSC is superior to ABC and HTCMIABC for unknown parameters and time-delays of the chaotic systems accurately and effectively. And it is a promising tool for chaotic system identification as well as other numerical optimization problems in mathematics.

► Identificate the uncertain parameters and time-delays of chaos system.
► Using novel artificial bee colony algorithm with space contraction.
► A mathematics models for chaos with nonnegative function’s minimums correspond to best combination of parameters and time-delay.
► Objective function analysis.