Related papers: Replicator equations and space
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator…
This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime…
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…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
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…
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 criteria…
In this paper we study a class of stationary states for reaction--diffusion systems of $k\geq 3$ densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide…
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…