Parrondo's paradox for chaos control and anticontrol of fractional-order systems

doi:10.1088/1674-1056/25/1/010505

中国物理B ›› 2016, Vol. 25 ›› Issue (1): 10505-010505.doi: 10.1088/1674-1056/25/1/010505

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

Marius-F Danca and Wallace K S Tang

1. Department of Mathematics and Computer Science, Avram Iancu University, 400380 Cluj-Napoca, Romania;
2. Romanian Institute for Science and Technology, 400487 Cluj-Napoca, Romania;
3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

收稿日期:2015-03-08 修回日期:2015-09-10 出版日期:2016-01-05 发布日期:2016-01-05
通讯作者: Marius-F Danca E-mail:danca@rist.ro

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

Marius-F Danca^1,2 and Wallace K S Tang³

1. Department of Mathematics and Computer Science, Avram Iancu University, 400380 Cluj-Napoca, Romania;
2. Romanian Institute for Science and Technology, 400487 Cluj-Napoca, Romania;
3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

Received:2015-03-08 Revised:2015-09-10 Online:2016-01-05 Published:2016-01-05
Contact: Marius-F Danca E-mail:danca@rist.ro

摘要/Abstract

摘要：

We present the generalized forms of Parrondo's paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N≥2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words “winning” and “loosing” in the classical Parrondo's paradox with “order” and “chaos”, respectively, the PS algorithm leads to the generalized Parrondo's paradox: chaos₁+chaos₂+…+chaos_N=order and order₁+order₂+…+order_N=chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system.

关键词: Parrondo', s paradox, chaos control, parameter switching algorithm, fractional-order Chen system

Abstract:

Key words: Parrondo', s paradox, chaos control, parameter switching algorithm, fractional-order Chen system

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.-a (Nonlinear dynamics and chaos)

Marius-F Danca, Wallace K S Tang. Parrondo's paradox for chaos control and anticontrol of fractional-order systems[J]. 中国物理B, 2016, 25(1): 10505-010505.

Marius-F Danca, Wallace K S Tang. Parrondo's paradox for chaos control and anticontrol of fractional-order systems[J]. Chin. Phys. B, 2016, 25(1): 10505-010505.

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Parrondo's paradox for chaos control and anticontrol of fractional-order systems

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

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