Synchronization of diffusively-coupled limit cycle oscillators

We develop analytical and numerical conditions to determine whether limit cycle oscillations synchronize in diffusively coupled systems. We examine two classes of systems: reaction–diffusion PDEs with Neumann boundary conditions, and compartmental ODEs, where compartments are interconnected through...

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Bibliographic Details
Published in:Automatica (Oxford) 2013-12, Vol.49 (12), p.3613-3622
Main Authors: Shafi, S. Yusef, Arcak, Murat, Jovanović, Mihailo, Packard, Andrew K.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Compartments
Computer science
control theory
systems
Control theory. Systems
Diffusion
Diffusively-coupled systems
Dynamical systems
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Limit cycles
Mathematical analysis
Mathematics
Nonlinear dynamics
Nonlinear dynamics and nonlinear dynamical systems
Optimal control
Oscillators
Partial differential equations
Physics
Sciences and techniques of general use
Solid mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Structural and continuum mechanics
Structured singular value
Synchronization
Synchronization
coupled oscillators
Time-varying systems
Trajectories
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:We develop analytical and numerical conditions to determine whether limit cycle oscillations synchronize in diffusively coupled systems. We examine two classes of systems: reaction–diffusion PDEs with Neumann boundary conditions, and compartmental ODEs, where compartments are interconnected through diffusion terms with adjacent compartments. In both cases the uncoupled dynamics are governed by a nonlinear system that admits an asymptotically stable limit cycle. We provide two-time scale averaging methods for certifying stability of spatially homogeneous time-periodic trajectories in the presence of sufficiently small or large diffusion and develop methods using the structured singular value for the case of intermediate diffusion. We highlight cases where diffusion stabilizes or destabilizes such trajectories.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.09.011