Báo cáo khoa học 演講訊息

For the stationary equations, We will describe basic local bifurcation theory based on implicit function theorem and global bifurcation theorem based on topological degree. Examples include Turing bifurcation induced by diffusion or cross-diffusion, loops of stationary solutions in predator-prey systems, and also bounded branch connecting semi-trivial solutions in predator-prey systems. We will also present Hopf bifurcation theorem for reaction-diffusion systems, including the case of delayed reaction-diffusion equations. In particular, we show the existence of spatial non-homogeneous periodic orbits in predator-prey systems. Global bifurcation of periodic orbits will also be discussed.