An Efficient Nonstandard Finite Difference Scheme for Chaotic Fractional-Order Chen System

IEEE Access

Liang Li¹  Beijia Wang¹  Yaowu Wang¹ 

[1] Key Laboratory of Structures Dynamic Behavior and Control, Ministry of Education, Harbin Institute of Technology, Harbin, China;

关键词: Fractional differential equations;    chaotic system;    nonstandard finite difference;    fractional derivative;    changeable memory;   

DOI  :  10.1109/ACCESS.2020.2996271

来源: DOAJ

【 摘 要 】

In this paper, an efficient nonstandard finite difference scheme for the numerical solution of chaotic fractional-order Chen system is developed. In the new method, an appropriate nonlocal framework in conjunction with the Grünwald-Letnikov approximation are applied for the discretization of fractional differential system. By constructing the discretization with the nonstandard finite difference scheme, high resolution of the system can be obtained, and the numerical instabilities of the nonlinear fractional-order Chen chaotic system can be also addressed to some extent. In addition, a new fractional derivative of the Caputo type is employed in the context of fractional-order Chen system to further decrease the computational complexity in the long-term treatment of fractional model. Numerical simulations demonstrate the applicability, accuracy and efficiency of the developed method.

【 授权许可】

Unknown