Open AccessStudy on a class of chaotic systems with fractional order
Author(s) -
Zhao Pin-Dong,
Xiaodan Zhang
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.2791
Subject(s) - attractor , chaotic , class (philosophy) , order (exchange) , synchronization of chaos , fractional order system , equivalence (formal languages) , equilibrium point , chaotic systems , stability (learning theory) , chaotic hysteresis , butterfly effect , mathematics , computer science , topology (electrical circuits) , statistical physics , fractional calculus , nonlinear system , control theory (sociology) , physics , pure mathematics , mathematical analysis , control (management) , quantum mechanics , combinatorics , finance , artificial intelligence , machine learning , economics
In this paper, a class of chaotic systems with fractional order is generalized and their topological equivalence is proved. It indicates that the necessary condition for a system with fractional order to generate chaotic attractor is to maintain the stability of the equilibrium points of the system. Numerical simulation shows that, similar to chaotic systems with integer order, the class of chaotic systems with fractional order can also generate a couple of double-scroll chaotic attractors.