A Hopf Bifurcation in a Radially Symmetric Interfacial Problem with Global Coupling

We consider an interfacial problem arising in reaction-diffusion models in an inhomogeneous media with global coupling. The purpose of this paper is to analyze the occurrence of Hopf bifurcation in the interfacial problem as the bifurcation parameters vary and to examine the effects of an inhomogeneous media and with the global coupling intensity in two- and three- dimensional system. Conditions for existence of stationary solutions and Hopf bifurcation for a certain class of inhomogeneity and global coupling are obtained analytically in two- and three- dimensional system with radial symmetry.