Dynamical system for animal coat pattern model

Abstract

We construct a dynamical system for a reaction diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of global positive strong solutions to the system by using semigroup methods. Second, we show that the solutions are continuously dependent on initial values. Third, we show that the dynamical system enjoys exponential attractors whose fractal dimensions can be estimated. Finally, we give a numerical example.