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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…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
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…
We consider the Taylor-Couette problem in an infinitely extended cylindrical domain. There exist modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow. These…
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…
We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability…
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species,…
We study spatial correlation effects in multiorbital systems, especially in a paramagnetic metallic state subject to Hund's coupling. We apply a cluster extension of the dynamical mean-field theory (DMFT) to the three-orbital Hubbard model…
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…
We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the…
Pattern dynamics on curved surfaces are ubiquitous. Although the effect of surface topography on pattern dynamics has gained much interest, there is a limited understanding of the roles of surface geometry and topology in pattern dynamics.…
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
Neuron is a noisy information processing unit and conventional view is that information in the cortex is carried on the rate of neurons spike emission. More recent studies on the activity propagation through the homogeneous network have…
This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…