Synchronization of limit cycle oscillations in diffusively-coupled systems

S. Yusef Shafi, Murat Arcak, Mihailo R. Jovanovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


We present analytical and numerical conditions to verify whether limit cycle oscillations synchronize in diffusively coupled systems. We consider both compartmental ODE models, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments, and reaction-diffusion PDEs with Neumann boundary conditions. In both the discrete and continuous spatial domains, we assume the uncoupled dynamics are determined by a nonlinear system which admits an asymptotically stable limit cycle. The main contribution of the paper is a method to certify when the stable oscillatory trajectories of a diffusively coupled system are robust to diffusion, and to highlight cases where diffusion in fact leads to loss of spatial synchrony. We illustrate our results with a relaxation oscillator example.

Original languageEnglish (US)
Title of host publication2013 American Control Conference, ACC 2013
Number of pages6
StatePublished - Sep 11 2013
Event2013 1st American Control Conference, ACC 2013 - Washington, DC, United States
Duration: Jun 17 2013Jun 19 2013


Other2013 1st American Control Conference, ACC 2013
Country/TerritoryUnited States
CityWashington, DC


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