On the shape of the stable patterns for activator-inhibitor systems


Prof. Yasuhito Miyamoto  ( Tokyo Institute of Technology, Japan )

2008 - 01 - 16 (Wed.)
14:10 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

It is well-known that every inhomogeneous steady state of a scalar reaction-diffusion equation with the Neumann boundary condition is unstable provided that the domain is convex. It is also known that if an inhomogeneous steady state of a shadow reaction-diffusion system in a finite interval is stable, then it is monotone. In this talk, we consider the shape of the stable steady states to a shadow reaction-diffusion system of activator-inhibitor type in a disk. In particular, we give necessary conditions for a steady state to be stable, which can be determined by the shape.