American Institute of Mathematical Sciences

Advanced
March  2007, 7(2): 275-284. doi: 10.3934/dcdsb.2007.7.275

A new mechanism of the chaos suppression

Arsen R. Dzhanoev 1, , Alexander Loskutov 1, , Hongjun Cao 2, and  Miguel A.F. Sanjuán 3,

1. 

Physics Faculty, Moscow State University, Moscow 119899, Russian Federation, Russian Federation
2. 

Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
3. 

Universidad Rey Juan Carlos, Departamento de Física, c/ Tulipán s/n 28933 Móstoles., Spain

Received  March 2006 Revised  September 2006 Published  December 2006

The standard Melnikov method for analyzing the onset of chaos in the vicinity of a separatrix is used to explore the possibility of suppression of chaos of a certain class of dynamical systems. For a given dynamical system we apply an external perturbation, which we call the stabilizing perturbation, with the goal that after its action the chaos present in the system is suppressed. We apply this method to the nonlinear pendulum as a paradigm, and obtain some analytical expressions for the corresponding external perturbations that eliminate chaotic behavior. Numerical simulations in the pendulum show a complete agreement with the analytical results.
Keywords: separatrix splitting, chaos suppression., Melnikov method.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Arsen R. Dzhanoev, Alexander Loskutov, Hongjun Cao, Miguel A.F. Sanjuán. A new mechanism of the chaos suppression. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 275-284. doi: 10.3934/dcdsb.2007.7.275
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