Eur. Phys. J. B (2012) 85: 230
https://doi.org/10.1140/epjb/e2012-21037-0

Regular Article

A detection method of symmetry restoration process of attractor merging crisis

¹ Department of Mathematical Sciences, Osaka Prefecture University, 599-8531 Sakai, Japan
² PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, 332-0012 Saitama, Japan
³ FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, 153-8505 Tokyo, Japan
⁴ Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, 153-8505 Tokyo, Japan

^a e-mail: gutchi@ms.osakafu-u.ac.jp

Received: 16 December 2011
Received in final form: 17 April 2012
Published online: 3 July 2012

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.