Fractional-order cuckoo search algorithm for parameter identification of the fractional-order chaotic, chaotic with noise and hyper-chaotic financial systems

Abstract Identifying the parameters of the chaos phenomena in the economic-financial systems is a critical issue to control and avoid the financial crises and bogging the market down. Therefore, in this paper, an efficient and reliable optimization algorithm is developed to identify the corresponding parameters of that chaotic dynamical behavior in the fractional-order chaotic, chaotic with noise, and hyper-chaotic financial systems. The introduced algorithm is a cooperation among the fractional calculus (FC) perspective and the basic cuckoo search algorithm to enhance the stochastic cuckoo’s walk via considering the cuckoo’s earlier behaviors from memory. The developed fractional-order cuckoo search (FO-CS) is validated with twenty-eight functions of CEC2017 with different dimensions. Several measures and non-parametric statistical tests are presented to demonstrate the superiority of the introduced algorithm while compared with the CS and the state-of-the-art techniques. The results show that merging of FC properties magnifies CS’s efficiency, convergence speed, and robustness against the complexity of the considered CEC benchmarks suite and the non-linearity of the fractional-order chaotic, chaotic with noise, and hyper-chaotic financial systems.

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