Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been ob...

Fluctuation Kinetics in a Multispecies Reaction-Diffusion System

We study fluctuation effects in a two species reaction-diffusion system, with three competing reactions A + A → ∅, B + B → ∅, and A + B → ∅. Asymptotic density decay rates are calculated for d ≤ 2 using two separate methods the Smoluchowski approximation, and also field theoretic/renormalisation group (RG) techniques. Both approaches predict power law decays, with exponents which asymptotically...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press

Reaction-Diffusion Systems in Epidemiology

A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion which depends upon the way the specific disease is communicated among different populations or subpopulations. Compartmental models describing a finite number of subpopulations can be described mathematically via systems of ordinary differ...