Fractional Order Generalization of a New Three-scroll Chaotic Chua System and Simulation

DOI

10.2991/lemcs-14.2014.76How to use a DOI?

Keywords

chaos;integral-order calculus, fractional-order calculus; chaotic Chua system;, three-scroll attractor

Abstract

Fractional-order differential systems are the generalization of integral-order differential systems that can be regarded as particular cases of the former. A three-scroll integral order chaotic Chua system and its generalization to fractional order are studied so as to construct a new fractional order Chua system. The theoretical analysis and numerical simulation of the new fractional Chua system dynamics are carried out. Fractional order range for system chaos generation is investigated and provided when integral order chaotic system being generalized to the fractional order systems, while the numeric simulation results are stated at the same time. The simulation results show that, with the decrease of fractional order, three-scroll attractor of integral-order system degenerates into two-scroll attractor of fractional-order system, then evolves into single-scroll periodic motion of two-scroll chaotic state, and finally trends towards the equilibrium point, i.e., the system features reverse Hopf bifurcation with which the equilibrium point area of chaotic attractor generation s will transfer.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xiaochun Liu
AU  - Dongping Hu
PY  - 2014/05
DA  - 2014/05
TI  - Fractional Order Generalization of a New Three-scroll Chaotic Chua System and Simulation
BT  - Proceedings of the International Conference on Logistics, Engineering, Management and Computer Science
PB  - Atlantis Press
SP  - 322
EP  - 326
SN  - 1951-6851
UR  - https://doi.org/10.2991/lemcs-14.2014.76
DO  - 10.2991/lemcs-14.2014.76
ID  - Liu2014/05
ER  -