Phase-Reduction Approach to Synchronization of Spatiotemporal Rhythms in Reaction-Diffusion Systems

Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffus...

Full description

Saved in:
Bibliographic Details
Published inPhysical review. X Vol. 4; no. 2; p. 021032
Main Authors Nakao, Hiroya, Yanagita, Tatsuo, Kawamura, Yoji
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 01.05.2014
Subjects
Biomedical engineering
Control methods
Differential equations
Diffusion
Dimensional stability
Dynamical systems
Dynamics
Ordinary differential equations
Oscillators
Reduction
Rhythm
Rotation
Spirals
Synchronism
Translating
Online AccessGet full text

Cover

More Information
Summary:Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffusion systems. However, the conventional phase-reduction theory, which provides a simple unified framework for analyzing synchronization properties of limit-cycle oscillators subjected to weak forcing, has mostly been restricted to low-dimensional dynamical systems. Here, we develop a phase-reduction theory for stable limit-cycle solutions of reaction-diffusion systems with infinite-dimensional state space. By generalizing the notion of isochrons to functional space, the phase-sensitivity function—a fundamental quantity for phase reduction—is derived. For illustration, several rhythmic dynamics of the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase-response properties and synchronization dynamics are revealed, reflecting their complex spatiotemporal organization. Our theory will provide a general basis for the analysis and control of spatiotemporal rhythms in various reaction-diffusion systems.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.4.021032