Inversion mechanism with functional extrema model for identification incommensurate and hyper fractional chaos via differential evolution

•Inversion mechanism with functional extrema model.•Identification of incommensurate and hyper fractional chaos.•Unknown fractional orders and systematic parameters.•Differential evolution algorithm.

In this paper, a novel uncertain fractional-orders and parameters’ inversion mechanism with functional extrema model via the differential evolution algorithms (DE) with a general mathematical model is proposed for incommensurate and hyper fractional chaotic systems. The problems of fractional-order chaos’ inversion estimation are converted into a functional extrema model in form of non-negative multiple modal objective functions’ minimization, which takes the unknown fractional-orders and parameters as its particular independent variables. And the objective is to find optimal combinations of fractional-orders and systematic parameters by DE in the predefined intervals for fractional order chaotic systems such that the objective function is minimized. Simulations are done to estimate a series of incommensurate and hyper fractional chaotic systems. And sensitivity analysis are also done in different cases for the proposed methods. The experiments’ results show that the proposed inversion mechanism for fractional-order chaotic systems is a successful methods with the advantages of high precision and robustness.