TRAVELING WAVES IN A REACTION-DIFFUSION SYSTEM MODELING FUNGAL MYCELIA

We discuss travelling-wave solutions of a system of coupled reaction-d iffusion equations used by the authors to describe the macroscopic beh aviour of fungal mycelia. Such systems have been used in a multitude o f applications; and, in particular, Merkin and Needham (1990, Proc. R. Sec. Lend. A 430, 315-45) have studied a certain formulation as a mod el for generic isothermal chemical reactions. We show that an alternat ive analysis provides more complete results in ascertaining the condit ions under which travelling-wave solutions exist and that it allows a wider range of parameter values to be considered; this is essential to the application considered in the present case. Numerical investigati ons of travelling-wave solutions and the related initial-value problem are included to motivate and extend the analysis.