Dynamics of self-excited oscillators with neutral delay coupling

Abstract

The work is devoted to analytic and numeric investigation of dynamical behavior in a system of two Van der Pol (VdP) oscillators coupled by a non-dispersive elastic rod. The model is rigorously reduced to a system of nonlinear neutral differential delay equations. For the case of relatively small coupling and moderate delay, an approximate analytic investigation can be accomplished by means of an averaging procedure. The region of synchronization in the space of parameters is established and characteristic bifurcations are revealed. A numeric study confirms the validity of the analytic approach in the synchronization region. Beyond this region, the averaging approach is no more valid. A multitude of quasiperiodic and chaotic-like orbits has been revealed. Especially interesting behavior occurs in the case of relatively large delays and corresponds to sequential quenching and excitation of the VdP oscillators. This regime is also explored analytically, by means of a large-delay approximation, which reduces the system to a perturbed discrete map.