Autonomous models on a Cayley tree

Abstract

.The most general single species autonomous reaction–diffusion model on a Cayley tree with nearest-neighbor interactions is introduced. The stationary solutions of such models, as well as their dynamics, are discussed. To study the dynamics of the system, we obtain a directionally symmetric Green function for the evolution equation of average number density. In some limiting cases the Green function is studied. Some examples are worked out in more detail.