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Chin. Phys. B, 2016, Vol. 25(1): 010505    DOI: 10.1088/1674-1056/25/1/010505
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Parrondo's paradox for chaos control and anticontrol of fractional-order systems

Marius-F Danca1,2 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

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+…+chaosN=order and order1+order2+…+orderN=chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system.

Keywords:  Parrondo'      s paradox      chaos control      parameter switching algorithm      fractional-order Chen system  
Received:  08 March 2015      Revised:  10 September 2015      Accepted manuscript online: 
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.-a (Nonlinear dynamics and chaos)  
Corresponding Authors:  Marius-F Danca     E-mail:

Cite this article: 

Marius-F Danca, Wallace K S Tang Parrondo's paradox for chaos control and anticontrol of fractional-order systems 2016 Chin. Phys. B 25 010505

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