ABSTRACT
In recent years many researchers have become interested in the existence and stability of periodic wavetrains for various reaction-diffusion systems. These systems are thought to be adequate models of various chemical and biological phenomena. This chapter shows that there are families of stable small amplitude waves bifurcating from the uniform rest state. It studies long waves which arise as the kinetic equations pass through a Hopf bifurcation. The chapter introduces a simple arbitrary reaction diffusion system for which linearized stability can be rigorously demonstrated.
