Related papers: Persistence versus extinction under a climate chan…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
We consider reaction-diffusion equations $\partial_tu=\Delta u+f(u)$ in the whole space $\mathbb{R}^N$ and we are interested in the large-time dynamics of solutions ranging in the interval $[0,1]$, with general unbounded initial support.…
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally…
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction-diffusion equation with strong Allee effect and free boundary. We give a description of the long-time…
Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence…
Spatial segregation occurs in population dynamics when $k$ species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of $k$ differential equations \[ -\Delta…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
We find a continuum of extinction rates for solutions $u(y,\tau)\ge 0$ of the fast diffusion equation $u_\tau=\Delta u^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $\ren$ for times up to the extinction time $T>0$.…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B + C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field approximation…
We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested…
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments.…
The dynamic nature of life's ability to thrive in diverse and changing planetary environments suggests that habitability and survival depend on the evolutionary path and life adaptation to environmental conditions. Here we explore such…
Two density-dependent branching processes are considered to model predator-prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
Population boundary is a classic indicator of climatic response in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental…
We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…