GENERATING CHAOTIC LIMIT CYCLES FOR A COMPLEX DUFFING–VAN DER POL SYSTEM USING A RANDOM PHASE

Yong Xu (), Wei Xu () and Gamal M. Mahmoud ()
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Yong Xu: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China
Wei Xu: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China
Gamal M. Mahmoud: Department of Mathematics, Faculty of Science, University of Assiut, 71516, Assiut, Egypt

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 09, 1437-1447

Abstract: Stochastic forces or random noises have been greatly used in studying the control of chaos of random real systems, but little is reported for random complex systems. Chaotic limit cycles of a complex Duffing–Van der Pol system with a random excitation is studied. Generating chaos via adjusting the intensity of random phase is investigated. We consider the positive top Lyapunov exponent as a criterion of chaos for random dynamical systems. It is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. We demonstrate the stable behavior of deterministic system when noise intensity is zero by means of the top (local) Lyapunov exponent. Poincaré surface analysis and phase plot are used to confirm our results. Later, random noise is used to generate chaos by adjusting the noise intensity to make the top (local) Lyapunov exponent changes from a negative sign to a positive one, and the Poincaré surface analysis is also applied to verify the obtained results and excellent agreement between these results is found.

Keywords: Complex dynamical system; chaos control; random phase; maximal Lyapunov exponent; stochastic bifurcation (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0129183105008023

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