Identification time-delayed fractional order chaos with functional extrema model via differential evolution

• Identification time-delayed fractional chaos.
• Inversion mechanism with functional extrema model.
• Differential evolution algorithm.
• Unknown time-delays, parameters and fractional-orders.
• Nonlinear optimization.

In this paper, a novel inversion mechanism of functional extrema model via the differential evolution algorithms (DE), is proposed to exactly identify time-delays fractional order chaos systems. With the functional extrema model, the unknown time-delays, systematic parameters and fractional-orders of the fractional chaos, are converted into independent variables of a non-negative multiple modal functions’ minimization, as a particular case of the functional extrema model’s minimization. And the objective of the model is to find their optimal combinations by DE in the predefined intervals, such that the objective functional is minimized. Simulations are done to identify two classical time-delayed fractional chaos, Logistic and Chen system, both in cases with noise and without. The experiments’ results show that the proposed inversion mechanism for time-delay fractional-order chaotic systems is a successful methods, with the advantages of high precision and robustness.