On global behaviour of the solutions of system of two Duffing–Van der Pole equations

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.