Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding "normal," diagonal diffusion coefficients in magnitude in systems that invo...

The paper studied the processes represented by a system of equations particular product parabolic type. For solution mutual diffusion problems, evaluations were obtained according to environmental parameters and dimensions space. Computational schemes, algorithms, software packages in programming environments developed, solutions visualized solve problems.

Cross-diffusion is one of the most important factors affecting formation and transition Turing patterns in reaction diffusion systems. In this paper, cross-diffusion introduced into a Brusselator model to investigate effects directivity density-dependence on pattern transition. space obtained by standard linear stability analysis, amplitude equations are derived based weakly nonlinear method, w...

This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the diffusion rates of individuals of two species depend on the concentration of individuals of the same species (self diffusion), or of the other species (cross d...

Cross diffusion is a phenomena in which a gradient in the concentration of one species induces a flux of another chemical species which was generally been neglected in the study of reaction-diffusion systems. We study the Turing bifurcation of two species reaction transport systems, where particle dispersal is governed by diffusion and cross diffusion. we performed linear stability analysis to ...

This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator–prey system in population–dynamics. The spatial movement of the capital and labour force are taken into account by cross–diffusion effect. First, we are showing two possible ways for modeling this system in only one country’s market (applying a simple functional response ...

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with selfand cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numer...