Time: 16:10-17:00

venue: Mathematics Building Room 527

Speaker: Prof. Toshiyuki Ogawa ( Meiji University, Tokyo )

Title: Pattern Dynamics Appearing on Compact Metric Graph

Abstract:

The study of reaction-diffusion equations on metric graph has been drawing attention recently. Here, we focus on pattern dynamics on compact metric graphs. There are eight different types of compact metric graphs which are constructed from two or three finite intervals. And we consider systems of reaction-diffusion equations on these compact metric graphs with natural boundary conditions. Suppose additionally the system has Turing or Wave instability. Then, by choosing the length of the segment intervals appropriately we have a degenerate situation, where we can use Fourier expansion. This enables us the normal form analysis to determine the local bifurcation structure around the bifurcation point.