相关论文: Dynamics of a diffusive predator-prey model: the e…

In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…

Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…

A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We…

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbours, we conclude that temporal…

This paper concerns with the global dynamics of classical solutions to an important alarm-taxis ecosystem, which demonstrates the behaviors of prey that attract secondary predator when threatened by primary predator. And the secondary…

We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…

Endangered populations often experience limited growth ability at low densities, a phenomenon described by the Allee effect. In this thesis, we investigate a predator-prey model incorporating the Allee effect within a two-dimensional…

We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…

In the current manuscript, we consider a predator-prey model where the predator is modeled as a generalist using a modified Leslie-Gower scheme, and the prey exhibits group defence via a generalised response. We show that the model could…

Theoretical models show that in a non-constant environment two predator species feeding on one and the same prey may coexist because the two species occupy different temporal niches: the one with the longer handling time has the advantage…

For a stationary system representing prey and $N$ groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if the number of components $N$ is too large or if the…

This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-global well-posedness and the large time behavior of solutions in a case where the habitat is a…

Complex adaptive systems have been the subject of much recent attention. It is by now well-established that members (`agents') tend to self-segregate into opposing groups characterized by extreme behavior. However, while different social…

A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We…

A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of…

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

This paper investigates a predator-prey reaction-diffusion model incorporating predator-taxis and a prey refuge mechanism, subject to homogeneous Neumann boundary conditions. Our primary focus is the analysis of codimension-two…

Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an…

We here discretize a predator-prey model by standard Euler forward method and non-standard finite difference method and then compare their dynamic properties with the corresponding continuous-time model. We show that NSFD model preserves…