Related papers: A free boundary problem for spreading under shifti…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…
We discuss a cellular automata model to study the competition between an emergent better fitted species against an existing majority species. The model implement local fights among small group of individual and a synchronous random walk on…
Population survival depends on a large set of factors that includes environment structure. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from…
In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime…
We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of pathogens: the wild type and the mutant. The system is of a…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
In this paper, we propose and analyze a nonlocal cooperative reaction--diffusion system with free boundaries and drift terms, motivated by directional epidemic spread. Lacking a variational structure but requiring sharper regularity of…
The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave…
We study the spread of a novel state in a network, in the presence of an exogenous control. The considered controlled evolutionary dynamics is a non-homogeneous Markov process that describes the evolution of the states of all nodes in the…
In this investigation we study the effects of climate change on predator-prey population dynamics. The interaction of predator and prey is described by the Variable Territory (VT) model with Allee effects in an Ordinary Differential…
Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…