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A novel artificial bee colony algorithm with space contraction for unknown parameters identification and time-delays of chaotic systems. (English) Zbl 1288.34068
Summary: 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.

MSC:
34K29 Inverse problems for functional-differential equations
34K35 Control problems for functional-differential equations
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
90C59 Approximation methods and heuristics in mathematical programming
Software:
ABC
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