Related papers: Patterns in Time and Space from a Single Morphogen…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact ``localized states." The formation of space-filling patterns from…
We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…
Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105…
In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets sharing two common modes. Our basic findings are the following. When spatial dependence is absent, the homogeneous manifold so obtained can be…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
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…
We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…