MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A geometric framework for phase synchronization in coupled noisy nonlinear systems

Janaki Balakrishnan


A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behavior through a change of stability via a Hopf bifurcation entails the spontaneous appearance of a gauge structure in the system, arising from the evolution of the slow dynamics, but induced by the fast variables. The conditions for the oscillators to be synchronised in phase are obtained. The role of weak noise appears to be to drive the system towards a more synchronized behavior. Our analysis provides a framework to explain recent experimental observations on noise-induced phase synchronization in coupled nonlinear systems.

05.45.-a, 05.45.Xt, 05.40.-a, 02.90.+p, 89.75.-k

Related publications

2006 Repository Open Access
Janaki Balakrishnan

Geometric framework for phase synchronization in coupled noisy nonlinear systems

In: Physical review / E, 73 (2006) 3, p. 036206