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Synchronization of Coupled Limit Cycles

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, PA, 19104, USA

    Georgi S. Medvedev

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  1. Georgi S. Medvedev
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Correspondence to Georgi S. Medvedev.

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Communicated by M. Golubitsky.

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Medvedev, G.S. Synchronization of Coupled Limit Cycles. J Nonlinear Sci 21, 441–464 (2011). https://doi.org/10.1007/s00332-010-9088-4

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  • DOI: https://doi.org/10.1007/s00332-010-9088-4

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