Speed selection in coupled Fisher waves
Martin Evans, University of Edinburgh, Institute for Condensed Matter and Complex Systems, School of Physics
The Fisher equation describes the spread of a population or the spread of an advantageous gene through a population. It is well known as a simple nonlinear equation which exhibits travelling wave solutions. Within statistical physics It has played a major role in our understanding of phase ordering dynamics and random first order phase transitions. In this talk we review the selection mechanism for the speed of the travelling waves which was established some time ago. We go on to consider two coupled Fisher equations representing two populations e.g. sub-populations of bacteria which are susceptible or resistant to antibiotic. We show that a subtle coupling between two population waves gives rise to a novel speed selection mechanism.