Bifurcation Analysis of Two Dissipatively Coupled van der Pol Oscillators

Authors investigate the dynamics of two coupled van der Pol oscillators. System demonstrates typical phenomena and bifurcation mechanisms that occur in different coupled self-oscillation systems with limit cycles. The case of dissipative coupling in the system causes suppression of oscillation, when growth of coupling parameter and non-identity of own frequences lead to suppression of oscillations in each self-oscillator. The description of dynamics of coupled oscillators was done for quasi-harmonic approximation near the point of Andronov-Hopf bifurcation with the transition to shorten amplitude and phase equations. This paper represents the results of bifurcation analysis of two coupled van der Pol oscillators as a full system of ordinary differential equations without quasi-harmonic approximation. It allows to use these results for comparison of theoretic and experimental data.