Numerical analysis of a simplest fractional-order hyperchaotic system  

作　　者：Dong Peng Kehui Sun Shaobo He Limin Zhang Abdulaziz O.A.Alamodi 

机构地区：[1]School of Physics and Electronics, Central South University

出　　处：《Theoretical & Applied Mechanics Letters》2019年第4期220-228,I0004,共10页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China (61161006 and 61573383);supported by the Research and Innovation Project of Graduate Students of Central South University (2018ZZTS348)

摘　　要：In this paper,a simplest fractional-order hyperchaotic(SFOH)system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system,which possesses seven terms without any quadratic or higher-order polynomials.The numerical solution of the SFOH system is investigated based on the Adomian decomposition method(ADM).The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics.Dynamics of this system are demonstrated by means of phase portraits,bifurcation diagrams,Lyapunov exponent spectrum(LEs)and Poincarésection.The results show that the system has a wide chaotic range with order change,and large Lyapunov exponent when the order is very small,which indicates that the system has a good application prospect.Besides,the parameter a is a partial amplitude controller for the SFOH system.Finally,the system is successfully implemented by digital signal processor(DSP).It lays a foundation for the application of the SFOH system.In this paper, a simplest fractional-order hyperchaotic(SFOH) system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system, which possesses seven terms without any quadratic or higher-order polynomials. The numerical solution of the SFOH system is investigated based on the Adomian decomposition method(ADM). The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics. Dynamics of this system are demonstrated by means of phase portraits, bifurcation diagrams, Lyapunov exponent spectrum(LEs) and Poincaré section. The results show that the system has a wide chaotic range with order change, and large Lyapunov exponent when the order is very small, which indicates that the system has a good application prospect. Besides, the parameter a is a partial amplitude controller for the SFOH system. Finally, the system is successfully implemented by digital signal processor(DSP). It lays a foundation for the application of the SFOH system.

关 键 词：CHAOS FRACTIONAL CALCULUS Simplest FRACTIONAL-ORDER HYPERCHAOTIC system Adomian decomposition method DSP implementation 

分 类 号：O3[理学—力学]