New Dynamical Mechanisms of Quenching in a System of Coupled Bautin Oscillators

A system of two diffusively coupled Bautin (generalized Stuart – Landau) oscillators is considered. Using a specially designed reduced system, the existence and stability of homogeneous solutions are investigated. Such solutions represent oscillatory regimes in which the amplitudes of different oscillators are identical to each other and coincide at any given time. A partition of “coupling strength — frequency mismatch” parameter plane into regions with different dynamical behavior of the oscillators is obtained. It is established that the phase space of the system has a foliation into a continuum of two-dimensional invariant manifolds. It is shown that oscillation quenching in the system, in contrast to systems of diffusively coupled Stuart – Landau oscillators, is determined by new mechanisms and is associated with the bifurcation of merger of invariant tori and the saddle-node (tangent) bifurcations of limit cycles. At the same time, the quenching does not occur monotonously with a change in the coupling strength, but abruptly, and the critical value of the coupling strength depends on the frequency mismatch between the oscillators.