Journal of Nonlinear Science

, Volume 21, Issue 3, pp 441–464 | Cite as

Synchronization of Coupled Limit Cycles



A unified approach to the analysis of 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 by a discussion of numerical simulations of a compartmental model of a neuron.


Synchronization Dissipative coupling Network Consensus protocol Compartmental model 

Mathematics Subject Classification (2000)

34D20 92C20 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsDrexel UniversityPhiladelphiaUSA

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