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A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors |
| Marius-F. Dancaa b, M. A. Aziz-Alaouic, Michael Smalld |
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 |
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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.
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Received: 07 November 2014
Revised: 30 December 2014
Accepted manuscript online:
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PACS:
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05.45.Ac
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(Low-dimensional chaos)
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05.45.Gg
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(Control of chaos, applications of chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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| Fund: Dedicated to Professor Chen Guan-Rong on the occasion of his 65th birthday. |
Corresponding Authors:
Marius-F. Danca, M. A. Aziz-Alaoui, Michael Small
E-mail: danca@rist.ro;aziz.alaoui@univ-lehavre.fr;michael.small@uwa.edu.au
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| About author: 05.45.Ac; 05.45.Gg; 05.45.Pq |
Cite this article:
Marius-F. Danca, M. A. Aziz-Alaoui, Michael Small A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors 2015 Chin. Phys. B 24 060507
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