Related papers: Spiraling asymptotic profiles of competition-diffu…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
For a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method allows us to identify relatively…
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed stationary solutions, showing that they are precisely circles…
We consider systems with two competing species whose actions are completely symmetric, with same mobility, reproduction and competition rates. Numerical implementations of the model in two and three-dimensional space show that regions of…
The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via timescale separation arguments. For neutral systems the two are found to be equivalent at long times. For systems with selective…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…
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…
We analyze the symmetry breaking of matter-wave solitons in a pair of cigar-shaped traps coupled by tunneling of atoms. The model is based on a system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs). Unlike the well-known…
In this paper, two competitive Lotka-Volterra populations in the two-patch-system with diffusion are considered. Each of the two spiecies can diffuse indepently and discretely between its in intrapatch and interpatch. By means of…
We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics structure with four…
We consider a class of nonautonomous parabolic competition-diffusion systems on bounded radial domains under Neumann boundary conditions. We show that, if the initial profiles satisfy a reflection inequality with respect to a hyperplane,…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems.…
In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed distribution of obstacles in the limit of low-volume fraction.…
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms. Assuming existence of traveling waves and enough…
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…
Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…
We present evidence that the concurrent existence of two populations of particles with different effective diameters is not a prerequisite for the occurrence of anomalous phase behaviors in systems of particles interacting through…