A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system

Advances in Difference Equations

Amin Jajarmi¹  Dumitru Baleanu²  Mehran Namjoo³  Sadegh Zibaei³ 

[1] Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran;Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia, Turkey;Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, 06530, Ankara, Turkey;Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran;

关键词: Fractional calculus;    Chaos;    Nonstandard finite difference scheme;    Nonidentical synchronization;    Active control;   

DOI  :  10.1186/s13662-021-03454-1

来源: Springer

【 摘 要 】

The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy.

【 授权许可】

CC BY