Traveling waves in coupled reaction-diffusion models with degenerate sources.
We consider a general system of coupled nonlinear diffusion equations that are characterized by having degenerate source terms and thereby not having isolated rest states. Using a general form of physically relevant source terms, we derive conditions that are required to trigger traveling waves when a stable uniform steady-state solution is perturbed by a highly localized disturbance. We show that the degeneracy in the source terms implies that traveling waves have a number of surprising properties that are not present for systems with nondegenerate source terms. We also show that such systems can lead to a pair of waves that initially propagate outwards from the disturbance, slow down, and reverse direction before ultimately colliding and annihilating each other.
Wylie
Jonathan J
JJ
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong. wylie@math.cityu.edu.hk
Miura
Robert M
RM
D000200:Action Potentials / Q000502:physiology*; D003198:Computer Simulation; D004058:Diffusion; D008564:Membrane Potentials / Q000502:physiology*; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology*; D009474:Neurons / Q000502:physiology*