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

¹ Semenov Institute of Chemical Physics Russian Academy of Sciences - Kosygin st., 4 Moscow, 119991 Russia
² Wayne State University - 1200 Holden Street, Detroit, MI 48202, USA

Received: 29 August 2017
Accepted: 3 January 2018

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.