Non-conventional phase attractors and repellers in weakly coupled autogenerators with hard excitation

TL;DR

This paper explores complex attractors and repellers in weakly coupled autogenerators with hard excitation, revealing new nonlinear synchronization phenomena and intricate phase space evolution.

Contribution

It introduces the discovery of non-conventional phase attractors and repellers in autogenerators, expanding understanding of nonlinear synchronization and phase space dynamics.

Findings

Identification of non-conventional attractors in coupled autogenerators

Detection of repellers separating limit cycles and equilibrium points

Complex evolution of phase portraits with changing system parameters

Abstract

In our earlier studies, we found the effect of non-conventional synchronization, which is a specific type of nonlinear stable beating in the system of two weakly coupled autogenerators with hard excitation given by generalized van der Pol-Duffing characteristics. The corresponding synchronized dynamics are due to a new type of attractor in a reduced phase space of the system. In the present work, we show that, as the strength of nonlinear stiffness and dissipation are changing, the phase portrait undergoes a complicated evolution leading to a quite unexpected appearance of difficult to detect repellers separating a stable limit cycle and equilibrium points in the phase plane. In terms of the original coordinates, the limit cycle associates with nonlinear beatings while the stationary points correspond to the stationary synchronous dynamics similar to the so-called nonlinear local modes.