Parameter identification of chaotic systems by hybrid Nelder–Mead simplex search and differential evolution algorithm

Parameter identification of chaotic systems is an important issue in nonlinear science and has attracted increasing interest from a variety of research and application fields. Essentially, parameter identification can be formulated as a multi-dimensional optimization problem. By combining differential evolution (DE) and Nelder–Mead (NM) simplex search, an effective hybrid algorithm named NMDE is proposed in this paper. By suitably fusing the DE-based evolutionary search and NM simplex-based local search, exploration and exploitation abilities can be well balanced and satisfactory optimization performances can be achieved. The NMDE hybrid algorithm is applied to parameter identification of several typical chaotic systems. Numerical simulation and comparisons with some typical existing algorithms demonstrate the effectiveness and robustness of the proposed hybrid NMDE algorithm. Moreover, the effects of noise and population size on the performances of NMDE are investigated as well.

Research highlights
► Parameter identification of chaotic systems.
► Nelder–Mead simplex search.
► Differential evolution.
► Hybrid algorithm.