ABSTRACT
In Chapter 2, reaction–diffusion modeling is presented to describe the diffusive dispersal of the population, developmental processes, pattern formation in a class of oscillating chemical reactions, fractal colony growth of biological species, tomography studies of microemulsions and selection criteria for patterns, etc. Different classifications, derivation of reaction–diffusion (RD) equation, and the hyperbolic RD equation are discussed. Analysis for the Turing instabilities of two-species RD systems is presented. The following single-species, two-species, and multiple-species reaction–diffusion models are analyzed for their analytical and numerical solutions: (i) Three single-species reaction–diffusion models (linear model of Kierstead and Slobodkin, nonlinear Fisher equation, and Nagumo equation); (ii) two-species predator–prey reaction–diffusion system; (iii) six models in Applications in Biochemistry – Belousov–Zhabotinsky Reaction–Diffusion Systems (Oregonator model, Brusselator model, Schnakenberg model, Lengyel–Epstein model, Sel’kov model, and Gray–Scott model); (iv) three models of multispecies reaction–diffusion models (Hastings–Powell model, modified Upadhyay–Rai model, and modified Leslie–Gower-type three-species model). These models are analyzed for the stability of equilibrium points, Turing instability, Hopf bifurcation, and pattern formations.
