Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition

A reaction-diffusion system coupled by two equations subject to homogeneous neumann boundary condition on one-dimensional spatial domain (0,l π) with l > 0 is considered. according to the normal form method and the center manifold theorem for reaction-diffusion equations,the explicit formulas determining the properties of hopf bifurcation of spatially homogeneous and nonhomogeneous periodic solutions of system near the constant steady state (0,0) are obtained. © 2015 c.-h. zhang and x.-p. yan.