A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain with 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 are obtained.
"Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition." J. Appl. Math. 2015 1 - 12, 2015. https://doi.org/10.1155/2015/657307