Quiescent phases with distributed exit times (Q414740)

The authors develop a system for the coupled dynamics of two phases with general exit distributions and then consider several special novel dynamical systems. The authors find that a quiescent phase does not destabilize the system in the sense that all eigenvalues with negative real parts remain in the left half plane of the complex plane, in general a weakly stable stationary point does not become asymptotically stable when a quiescent phase is introduced, and in the particular case of a Dirac distribution such stabilization need not occur. Finally, some of the results are applied to traveling fronts in reaction diffusion equations with quiescent phase, and the explicit formula for the minimal speed of traveling fronts shows the slowing effect of the quiescent phase. This paper improves related results in the literature.