THE CONTROL OF STOCHASTIC COMPLEX DAMPED NONLINEAR SYSTEMS

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

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 08, 1263-1275

Abstract: The aim of this paper is to continue our investigations by studying complex damped nonlinear systems with random noise. The effect of random phase for these systems is examined. The interested system demonstrates unstable periodic attractors when the intensity of random noise equals zero, and we show that the unstable dynamical behavior will be stabilized as the intensity of random noise properly increases. The phase plot and the time evolution are carried out to confirm the obtained results of Poincaré map analysis and top Lyapunov exponent on the dynamical behavior of stability. Excellent agreement is found between these results.

Keywords: Complex damped dynamical system; top Lyapunov exponent; Poincaré map analysis; random phase; stabilization; time evolution (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107011303

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