On the question of the periodic solutions of a system of differential equations describing the oscillations of two loosely coupled Van der Pol oscillators

We study a system of two weakly coupled completely identical van der Pol oscillators in the case of diffusion coupling. the question of the existence and stability of periodic solutions of the system under consideration. It is shown that it can have periodic solutions of three types, which generate Andronov-Hopf cycles, antiphase, and the third type of synchronization cycles: asymmetric cycles. The analysis of the problem used the Poincare-Dulac method of normal forms, as well as the method of integral manifolds.