Parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems via a hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm

Hyperchaos can be observed in fractional-order nonlinear systems with suitable orders. The knowledge about systematic parameters and fractional orders is important for control and synchronization of fractional-order hyperchaotic systems. In this article, parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems is investigated. Firstly, estimation of systematic parameters and fractional orders is formulated as a multi-dimensional optimization problem by treating the fractional orders as additional parameters. Secondly, a novel method called hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm is proposed to deal with this optimization problem. Finally, numerical simulations and comparisons with other typical algorithms are done to demonstrate the effectiveness of the proposed algorithm, which provides a promising tool for estimation of fractional-order arbitrary dimensional hyperchaotic systems as well as other numerical optimization problems in different fields.