Resonance behaviour and jump phenomenon in a two coupled Duffing–van der Pol oscillators

We consider a two coupled Duffing–van der Pol oscillators with a nonlinear coupling. The method of multiple scales is used to obtain a set of autonomous equations for the amplitudes and phases of the response of the system. The stability boundaries of fixed points of the approximate equations are obtained using Routh–Hurwitz criterion. The stability boundaries are drawn in various parameters space. The influence of nonlinear damping, detuning, nonlinearity and the coupling strength on the response dynamics is studied. Jump phenomenon is found to occur for a range of values of the parameters of the system. The results obtained from the approximate equations are verified by numerically solving the original system and good agreement is obtained.