Abstract

A brief description of the model equations and their underlying physical basis is given. The space independent problem of a previous paper is extended to include diffusive processes. Trav-elling wave solutions are introduced, the stability of the steady states and the different bifurca-tion schemes are discussed. The collapse of the limit cycle, by means of an external stimulation or by internal constraints as well as the onset of propagating pulses is considered. Phase portraits are discussed in great detail. Correspondence between some approximated versions of the model equations and nervous pulse propagation equations is established. Furthermore, some suggestions for an experimental proof of the model are made.