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Multiparametrical optimal correction for chaos suppression in a family of Duffing-van der Pol oscillators

Yury Talagaev, Andrey Tarakanov
A technique of chaos suppression in chaotic dynamical systems presented in this paper is based on the idea of multiparametrical correction of the system’s parameters. The aim of correction is the chaotic system stabilization so that with the natural demand of minimal dynamic change of its parameters the modification of system’s chaotic attractor into the stable limit set will be provided. The words “minimal changing” mean that the feature of proposed technique lies in providing the achievement of an optimum regime by the system. This regime can be obtained with Pontryagin maximum principle under special kind of dynamic changing of parameters. The optimal corrective function can be found for each parameter. The value of these functions is the possibility to localize the unique limit set in the phase space of the system and to investigate the peculiarities of the optimal transient process which provides the modification of chaotic attractor into this set. The results of numerical experiments with the family of nonlinear oscillators have confirmed the quality of chaos suppression and efficiency of the offered technique.
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