Autonomous models on a Cayley tree
Mohammad Khorrami, Amir Aghamohammadi
TL;DR
This paper introduces a comprehensive autonomous reaction-diffusion model on a Cayley tree, analyzing its stationary states and dynamics through Green functions, with detailed examples and limiting case studies.
Contribution
It presents the most general single species autonomous reaction-diffusion model on a Cayley tree with new analytical solutions for dynamics and stationary states.
Findings
Derived the Green function for the evolution of average number density.
Analyzed stationary solutions and their stability.
Provided detailed examples and limiting case analyses.
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 dynamics of the system, directionally-symmetric Green function for evolution equation of average number density is obtained. In some limiting cases the Green function is studied. Some examples are worked out in more detail.
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