相关论文: Protection zone in a diffusive predator-prey model…
Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…
The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + \chi v^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u(m_1-u+av), \qquad & x\in\Omega, \ t>0, \\ v_t &=&…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
Pattern formation analysis of eco-epidemiological models with cannibalism and disease has been less explored in the literature. Therefore, motivated by this, we have proposed a diffusive eco-epidemiological model and performed pattern…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different…
In freshwater ecosystems, aquatic insects that ontogenetically shift their habitat from aquatic to terrestrial play vital roles as prey subsidies that move nutrients and energy from aquatic to terrestrial food webs. As a result, these…
This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…
We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving…
This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
This study investigates an SEIS PDE model with a free boundary, which captures the dynamics of epidemic transmission, including diseases like COVID-19. This parabolic PDE system is analyzed in a rotationally symmetric domain, and the…