Dynamic preserving method with changeable memory length of fractional-order chaotic system

Abstract

In this paper, an asymptotically stability condition α+β≥3γ of the fractional-order Lü system is proposed by using the theory of stability. Under this asymptotically stability condition and the Riemann-Liouville fractional derivative definition, the numerical efficiency is obtained by combining the nonstandard finite difference method with the Grünwald-Letnikov method. In addition, the reported dynamic preserving properties of the nonstandard finite difference method are verified by comparing with the predictor-corrector algorithm. Moreover, in order to reduce the computation time of fractional derivatives, a model with changeable memory length of short memory principle is introduced and solved by the nonstandard finite difference method. In the numerical examples, about 30% of computation time can be reduced by applying the changeable memory length model.