相关论文: Asymptotic spreading of interacting species with m…

This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…

We study the diffusive logistic equation with a free boundary in timeperiodic environment. To understand the effect of the dispersal rate $d$, the original habitat radius $h_0$, the spreading capability $\mu$, and the initial density $u_0$…

We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-Fokker-Planck type, is introduced via the associated entropy…

We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $\alpha$. Starting from an initial…

The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…

We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…

We present a new method for proving sharp local propagation of chaos in Fisher Information for particles with smooth interaction and drift. We rely on a new Lemma computing the Fisher Information of two diffusion processes with smooth…

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< \alpha\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with…

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via…

In this paper, we investigate the spreading properties of solutions of farmer and hunter-gatherer model which is a three-component reaction-diffusion system. Ecologically, the model describes the geographical spreading of an initially…

We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fractional Laplacian. Contrary to what happens in the standard…

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the…

We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…

We introduce a model for information spreading among a population of N agents diffusing on a square LxL lattice, starting from an informed agent (Source). Information passing from informed to unaware agents occurs whenever the relative…

The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…

This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence…

Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…