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 non–dispersive elastic rod. The model is rigorously described by the system of nonlinear neutral differential delay equations. For the case of relatively small coupling and moderate delay, an approximate analytic investigation is performed by means of averaging procedure. If the effective coupling remains small if the system is far from the internal resonance (sine in the denominator is not small). Region of synchronization in the space of parameter is established and characteristic bifurcations are revealed. Numeric study confirms the validity of the analytic approach in the synchronization region. Beyond this region the analytic approach is no more valid. Multitude of quasiperiodic and chaotic – like orbits has been revealed. Especially interesting behavior corresponds to sequential quenching and excitation of the VdP oscillators. This regime is also explored analytically, by means of large – delay approximation, which reduces the system to perturbed discrete map.