Coupled van der Pol–Duffing oscillators: Phase dynamics and structure of synchronization tongues

Synchronization in the system of coupled non-identical non-isochronous van der Pol–Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler’s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (non-isochronism of the oscillators, their non-identity, coupling of the dissipative and inertial types). Characteristic symmetries are revealed for the Adler’s equation responsible for equivalence of some of the factors. Numerical study of the parameters space of the initial differential equations is carried out using the method of charts of dynamic regimes in the parameter planes. Results obtained by both these approaches are compared and discussed.