A detection method of symmetry restoration process of attractor merging crisis

Abstract

We propose a method to detect the approach to a specific unstable symmetric mediating solution, which characterises the symmetry restoration process close to a bifurcation point of an attractor merging crisis. This method captures a temporary restoration of the symmetry, and it does not require neither the exact parameter value of the bifurcation point nor the mediating solution. We study a forced XY model as an example and show that this method figures out the singularity caused by the approach from the asymmetric side of the crisis. An analysis of the repulsively coupled Stuart Landau system suggests the feasibility of this method even when the mediating solution is a symmetric torus.