Related papers: Multiple diffusion scales and diffusion-driven ins…
Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
How patterns and structures undergo symmetry breaking and self-organize within biological systems from initially homogeneous states is a key issue for biological development. The activator-inhibitor (AI) mechanism, derived from…
Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…
Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…
We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift…
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…