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Parameter estimation is an important issue in nonlinear science, which can be formulated as a multi-dimensional problem. Numbers of nature-inspired meta-heuristic algorithms have been applied for parameter estimation of chaotic systems; however, many of them are not able to achieve an appropriate trade-off between exploration and exploitation. Therefore, this paper proposes an effective hybrid cuckoo search (HCS) algorithm to obtain higher quality solutions and convergence speed. Inspired by the powerful efficiency of differential evolution, the proposed HCS provides two novel mutation strategies to fully exploit the neighborhood among the current population. Furthermore, a crossover operator under self-adaptive parameters control is introduced to balance the exploration and exploitation ability of the proposed two mutation strategies. Besides, the opposition-based learning is incorporated into HCS for initializing population and producing new candidate solutions during the evolutionary process. HCS is further employed to estimate the unknown parameters and time delays of chaotic systems. Numerical simulations and comparisons with some other optimization methods are conducted on three chaotic systems with and without time delays to demonstrate the performance of HCS. The experimental results show a superiority of HCS in parameter estimation of chaotic systems, and can be regarded as a promising method in terms of its high calculation accuracy, fast convergence speed, and strong robustness.

An Effective Hybrid Cuckoo Search Algorithm for Unknown Parameters and Time Delays Estimation of Chaotic Systems