A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

doi:10.1088/1674-1056/24/6/060507

中国物理B ›› 2015, Vol. 24 ›› Issue (6): 60507-060507.doi: 10.1088/1674-1056/24/6/060507

A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

Marius-F. Danca^{a b}, M. A. Aziz-Alaoui^c, Michael Small^d

a Department of Mathematics and Computer Science, Emanuel University of Oradea, 410597 Oradea, Romania;
b Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania;
c Normandie University, France; ULH, LMAH, F-76600 Le Havre; FR CNRS 3335, ISCN, 25 rue Philippe Lebon 76600 Le Havre, France;
d School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia

收稿日期:2014-11-07 修回日期:2014-12-30 出版日期:2015-06-05 发布日期:2015-06-05
基金资助:
Dedicated to Professor Chen Guan-Rong on the occasion of his 65th birthday.

A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

Marius-F. Danca^{a b}, M. A. Aziz-Alaoui^c, Michael Small^d

a Department of Mathematics and Computer Science, Emanuel University of Oradea, 410597 Oradea, Romania;
b Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania;
c Normandie University, France; ULH, LMAH, F-76600 Le Havre; FR CNRS 3335, ISCN, 25 rue Philippe Lebon 76600 Le Havre, France;
d School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia

Received:2014-11-07 Revised:2014-12-30 Online:2015-06-05 Published:2015-06-05
Contact: Marius-F. Danca, M. A. Aziz-Alaoui, Michael Small E-mail:danca@rist.ro;aziz.alaoui@univ-lehavre.fr;michael.small@uwa.edu.au
About author:05.45.Ac; 05.45.Gg; 05.45.Pq
Supported by:
Dedicated to Professor Chen Guan-Rong on the occasion of his 65th birthday.

摘要/Abstract

摘要： In this paper we present a new version of Chen's system: a piecewise linear (PWL) Chen system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small parameter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.

关键词: PWL Chen attractor of fractional-order, parameter switching, Cellina', s Theorem, Filippov regularization, Sigmoid function, bifurcation diagram

Abstract: In this paper we present a new version of Chen's system: a piecewise linear (PWL) Chen system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small parameter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.

Key words: PWL Chen attractor of fractional-order, parameter switching, Cellina's Theorem, Filippov regularization, Sigmoid function, bifurcation diagram

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)

Marius-F. Danca, M. A. Aziz-Alaoui, Michael Small. A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors[J]. 中国物理B, 2015, 24(6): 60507-060507.

Marius-F. Danca, M. A. Aziz-Alaoui, Michael Small. A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors[J]. Chin. Phys. B, 2015, 24(6): 60507-060507.

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A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

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