Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems

Abstract

Optimization of the stability of synchronized states between a pair of symmetrically coupled reaction-diffusion systems exhibiting rhythmic spatiotemporal patterns is studied in the framework of the phase reduction theory. The optimal linear filter that maximizes the linear stability of the in-phase synchronized state is derived for the case where the two systems are linearly coupled. The nonlinear optimal interaction function that theoretically gives the largest linear stability of the in-phase synchronized state is also derived. The theory is illustrated by using typical rhythmic patterns in FitzHugh-Nagumo systems as examples.

arXiv comment18 pages, 14 figures, revised version, to be published in PRE

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Cited by in corpus (11)

• On the Concept of Dynamical Reduction : The Case of Coupled Oscillators
• Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory
• Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations
• Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling
• Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators
• Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators
• Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns
• Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
• Sparse optimization of mutual synchronization in collectively oscillating networks
• Phase reduction analysis of traveling breathers in reaction--diffusion systems
• Phase reduction of reaction-diffusion systems with delay