相关论文: Conditions for spatial instabilities and pattern f…

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…

Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…

In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…

Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…

The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…

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…

We apply tools from real algebraic geometry to the problem of multistationarity of chemical reaction networks. A particular focus is on the case of reaction networks whose steady states admit a monomial parametrization. For such systems we…

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…

Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…

For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…

We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…

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…

Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

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…

Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…