Related papers: Isolating Patterns in Open Reaction-Diffusion Syst…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which…
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 prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
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…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…
We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their…
By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes,…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…