A geometric framework for phase synchronization in coupled noisy nonlinear systems
J. Balakrishnan
Abstract
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 behaviour 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 behaviour. Our analysis provides a framework to explain recent experimental observations on noise-induced phase synchronization in coupled nonlinear systems.
Create a lesson
Related papers
Low-Dimensional Reduction Theory for Populations of Phase Oscillators with a Gaussian Frequency Distribution
Kai Tokunaga
Asymmetric Coupling Anisotropy for Causal Information Filtering in Physical Reservoirs
Takashi Hikihara, Yuma Aoki
Mixed-mode bursting oscillations in a three-timescale biophysical neuronal oscillator model
Ngoc Anh Phan, Yangyang Wang
Topology-Biased Resource Constraints Shape Synchronization Pathways in Hindmarsh-Rose Oscillator Networks
Zhouqi Li, Xiaoyan He, Yuanhong Bi et al.
Inertial synchronization of networked oscillators in arbitrary dimensions
Kirill Kovalenko, Bruce X. Dai, Fanshu Fang et al.
Thermodynamic criticality of coupled oscillators
Suvam Pal, Sudipta Mukherji, Jurgen Kurths et al.