Description of Research Area

Dynamics and Control of Rhythmic Spatiotemporal Patterns in Non-Equilibrium Systems

Research Subject

Spatiotemporal patterns in non-equilibrium dissipative systems have been extensively studied in chemical and biological systems. In particular, formation of rhythmic spatiotemporal patterns such as target and spiral waves is a generic property of oscillatory or excitable active media and can be observed in various real-world systems. Such systems are generally modeled by nonlinear partial differential equations, e.g., reaction-diffusion equations or fluid equations, which are difficult to analyze. However, in some situations, it is possible to systematically approximate the original models by low-dimensional ordinary differential equations, and such methods are called reduction theories. This research project aims to construct a reduction theory that is generally applicable to spatiotemporal rhythmic patterns in non-equilibrium systems, reveal their dynamics and response properties, and develop efficient control methods.