MULTISCALE PROPAGATION PHENOMENA IN REACTION-DIFFUSION SYSTEMS

Asymptotic methods and phase-plane analysis are combined to investigate existence and stability of various kinds of propagating fronts in nonlinear reaction-diffusion systems with widely separated characteristic time and length scales associated with different reactants. A basic difference is observed between two types of kinetic systems, called anticlinal and synclinal. This distinction is further traced down to processes of nucleation, excitation, and polarization of alternative steady states. The described phenomena include entrained, spearhead, shielding, and dragged fronts in infinite regions; travelling pulses and chaotic excitations in metastable systems; steady and undulating fronts in finite regions; mutual chase and split (synchronized) fronts in kinetic systems with several homogeneous steady states. © 1979 American Institute of Physics.