Analysis of hysteretic reaction-diffusion systems

Analysis of Hysteretic Reaction-diffusion Systems

In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlin...

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...

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

Nonlinear analysis of stationary patterns in convection-reaction-diffusion systems

Olga A. Nekhamkina, Alexander A. Nepomnyashchy, Boris Y. Rubinstein, and Moshe Sheintuch Department of Chemical Engineering, Technion–IIT, Technion City, Haifa 32 000, Israel Department of Mathematics, Technion–IIT, Technion City, Haifa 32 000, Isreal Minerva Center for Research in Nonlinear Phenomena, Technion–IIT, Technion City, Haifa 32 000, Israel ~Received 16 June 1999; revised manuscript ...

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