Cross-Diffusion Induced Instability and Stability in Reaction-Diffusion Systems

Mathematical analysis of a tumour-immune interaction model: A moving boundary problem

“…We determine conditions for the formation of Turing patterns by perturbing the stable tumour-dormant state with small heterogeneous perturbations [49,50]. It is important to note that, for simplicity, Turing instability analysis was carried out for the model without chemotaxis (i.e β∇ • (X .∇U) = 0) and on a fixed domain (i.e with the radius not depending on time).…”

Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System

“…Spatiotemporal pattern formation is a common phenomenon such as convection, chemical reactions, vegetation, vertebrate skin, plankton and so on [1-6, 9-13, 17]. Turing instability [5] play important roles to explain spatiotemporal patterns formation and many studies have focused on the mechanism behind the formation of regular patterns [6,9,[11][12][13]. Most reaction-diffusion models for pattern formation have used Neumann boundary conditions [6,8,12,13]…”

“…Turing instability [5] play important roles to explain spatiotemporal patterns formation and many studies have focused on the mechanism behind the formation of regular patterns [6,9,[11][12][13]. Most reaction-diffusion models for pattern formation have used Neumann boundary conditions [6,8,12,13]…”

“…Recently, a large number of papers investigate pattern formation in reaction-diffusion systems including linear and nonlinear cross-diffusion [10,12,13]. Some of these self-organized patterns have been attributed to the advection and cross-advection in the model with activator-inhibitor or positive-feedback reaction kinetics [1-4, 11, 17].…”