Normal forms of Hopf bifurcation for a reaction-diffusion system subject to Neumann boundary condition (Q2336942)

Summary: A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain \((0, \ell \pi)\) with \(\ell > 0\) 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.