Global Coupling of an Interface Problem in an Activator-inhibitor System (Journal of Partial Differential Equations, 2003)
" An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling."
Keywords: activator-inhibitor; van der Pol equation; global coupling; free boundary problem; Hopf bifurcation