MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER-MEINHARDT MODEL OF MORPHOGENESIS

A reaction-diffusion Gierer-Meinhardt model of morphogenesis subject to Dirichlet fixed boundary condition in the one-dimensional spatial domain is considered. We perform a detailed Hopf bifurcation analysis and steady state bifurcation analysis to the system. Our results suggest the existence of spatially nonhomogenous periodic orbits and nonconstant positive steady state solutions, which imply the possibility of complex spatiotemporal patterns of the system. Numerical simulations are carried out to support our theoretical analysis.