Roman Kondrashov

    Nizhny Novgorod, 603950, Gagarin av., 23
    Department of Mathematics and Mechanics, Nizhny Novgorod State University


    Kondrashov R. E., Morozov A. D.
    The problem of global behavior of solutions in system of two Duffing–Van der Pole equations close to nonlinear integrable is considered. For regions without unperturbed separatrixes we give partially averaged systems which describe the behavior of solutions of original system in resonant zones. The finiteness of number of non-trivial resonant structures is established. Also we give fully averaged systems which describe the behavior of solutions outside of neighborhoods of nontrivial resonant structures. The results of numerically investigation of these systems are resulted.
    Keywords: limit cycles, resonances, averaging
    Citation: Kondrashov R. E., Morozov A. D.,  On global behaviour of the solutions of system of two Duffing–Van der Pole equations, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  437-449
    Kondrashov R. E., Morozov A. D.
    We consider a problem about interaction of the two Duffing—van der Pol equations close to nonlinear integrable. The average systems describing behaviour of the solutions of the initial equation in resonant zones are deduced. The conditions of existence of not trivial resonant structures are established. The results of research in cases are resulted, when at the uncoupled equations exist and there are no limiting cycles.
    Keywords: limit cycles, resonances
    Citation: Kondrashov R. E., Morozov A. D.,  On investigation of resonances in system of two Duffing–van der Pol equations, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 2, pp.  241-254

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