Bifurcation diagram of the self-sustained oscillation modes for a system with dynamic symmetry

Abstract

An autonomous dynamical system with one degree of freedom is considered which possesses properties such that an asymptotically stable equilibrium becomes unstable after a certain parameter passes through zero and two new symmetrically arranged equilibria are created alongside it. It is known that, for sufficiently small values of the above mentioned parameter, bifurcation can be accompanied by the occurrence of periodic trajectories (cycles). To describe them, a bifurcation diagram of the relation between the amplitude of the cycles and the parameter, which characterizes the dissipation and takes finite values, is constructed. The results obtained are illustrated using the example of an investigation of the self-induced oscillatory modes in a model of an aerodynamic pendulum that takes account of the displacement of the pressure centre when the angle of attack is changed.