The problem of global behavior of solutions in system of two Duffing - van der Pol equations close to nonlinear integrable ones is considered. For regions without unperturbed separatrixes, partially averaged systems which describe the behavior of solutions of original system in resonant zones are investigated. The finiteness of the number of non-trivial resonant structures is established. Fully averaged systems which describe the behavior of solutions outside the vicinity of non-trivial resonant structures are also investigated. In the vicinity of unperturbed separatrixes the question of existence of a homoclinic Poincare structure is considered. Numerical results illustrate and confirm the theoretical results.
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