Related papers: Dynamics for a Ratio-dependent Prey-predator Model…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
There are many positive and negative factors present in the predator-prey interaction which affect the net growth of the species. Fear of predation is one such factor that creates psychological stress in a prey species, which causes a…
We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models' ability to fit data on freshwater plankton. We model the predator's switch from one prey to the other in…
As humans perceive and actively engage with the world, we adjust our decisions in response to shifting group dynamics and are influenced by social interactions. This study aims to identify which aspects of interaction affect…
We consider the model of spatially distributed population consisting of two species with "\textsl{predator\,--\,prey}" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not…
We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. In Part 1 (see \cite{ddl}) we have established a theory on the…
Predicting the evolution of expanding population is critical to control biological threats such as invasive species and virus explosion. In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the…
A generalized seasonally-varying predator-prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the trophic…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of…
We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing…
We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one,…
We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To…
A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…