Fractional-order Chua’s system: discretization, bifurcation and chaos

Advances in Difference Equations

Ravi P Agarwal¹  Sanaa M Salman²  Ahmed M A El-Sayed³ 

[1] Department of Mathematics, Texas A and M University, Kingsville, USA;Faculty of Education, Alexandria University, Alexandria, Egypt;Faculty of Science, Alexandria University, Alexandria, Egypt

关键词: Chua’s system;    fractional-order differential equations;    fixed points;    asymptotic stability;    chaotic attractor;    bifurcation;    chaos;   

DOI  :  10.1186/1687-1847-2013-320

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we are interested in the fractional-order form of Chua’s system. A discretization process will be applied to obtain its discrete version. Fixed points and their asymptotic stability are investigated. Chaotic attractor, bifurcation and chaos for different values of the fractional-order parameter are discussed. We show that the proposed discretization method is different from other discretization methods, such as predictor-corrector and Euler methods, in the sense that our method is an approximation for the right-hand side of the system under study.

【 授权许可】

CC BY