Synchronization of coupled limit cycles

Abstract

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.

Journal of Nonlinear Science, accepted

References in corpus (3)

• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Semi-passivity and synchronization of diffusively coupled neuronal oscillators
• Synchronization of coupled stochastic limit cycle oscillators

Cited by in corpus (8)

• Mathematical frameworks for oscillatory network dynamics in neuroscience
• The Poincare map of randomly perturbed periodic motion
• Nonlinear phase-amplitude reduction of delay-induced oscillations
• The geometry of spontaneous spiking in neuronal networks
• Synchronization Probability in Large Random Networks
• Shaping bursting by electrical coupling and noise
• Synchronization of coupled chaotic maps
• Suppression of Chaos in Mutually Coupled Synchronized Generalized Lorenz Systems