一类具有时滞的比率依赖型捕食者-食饵系统周期正解的存在性

考虑一类具有时滞的比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理,得到系统存在正周期解的充分条件.     

基于比率的三种群捕食者-食饵扩散系统的周期解

本文研究一类基于比率的三种群捕食者-食饵扩散系统,利用重合度理论建立了这类系统正周期解的存在性结果。     

带阶段结构的扩散的捕食者-食饵模型解的一致有界性和整体存在性

应用能量估计和Gagliardo-Nirenberg型不等式证明了捕食者带阶段结构的具有自扩散和交错扩散的捕食者-食饵模型解的一致有界性和整体存在性.     

具有扩散和比率依赖的三种群混合模型的分析

本文讨论了捕食者具有比率依赖的功能性反应,食饵与另一种群竞争且自身可以 扩散的混合模型.证明了系统一致持久与扩散有关,而且得到了系统存在全局吸引周期 解的充分条件.     

一类具有阶段结构的三次捕食者-食饵交错扩散系统的整体解

应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性,该系统是具有阶段结构的两种群Lotka-Volterra捕食者-食饵交错扩散模型的推广.通过构造Lyapunov函数给出了该系统正平衡点全局渐近稳定的充分条件.     

时间测度上具有时滞基于半比率的捕食者-食饵扩散系统的周期解

在时间测度上研究一类具有时滞和基于半比率且有功能性反应的两种群捕食者-食饵扩散系统,利用Mawhin重合度理论建立了这类系统的周期解存在的一个充分性判据.从而使这一类系统的连续与离散情形即相应的微分方程和差分方程的周期解存在性问题得到了统一研究.     

具有时滞和基于比率的两种群捕食者-食饵扩散系统的周期解

本文研究了一类具有时滞和基于比率的两种群捕食者—食饵扩散系统，利用重合度理论建立了这类系统正周期解的存在性判据。     

带Beddington-DeAngelis功能反应项的捕食者-食饵交错扩散模型整体解的存在性

本文采用能量方法和Bootstrap技巧证明了当空间维数n＜10时一类带Beddington-DeAngelis功能反应项的捕食者-食饵交错扩散模型整体解的存在性.     

具有Holling-II型功能反应和交叉扩散的捕食-食饵模型正平衡解的存在性和不存在性

本文主要研究一类在齐次Dirichlet边界条件下带交叉扩散的Holling-II型捕食者-食饵模型正平衡解的存在性, 其中两个交叉扩散系数分别代表食饵远离捕食者的趋势和捕食者追逐食饵的趋势. 应用不动点指标理论得到了正平衡解存在的充分条件, 并进一步研究了正平衡解不存在的条件.     

一类新的捕食模型的一致持久

研究了捕食者具阶段结构且食饵和捕食者具比率依赖的的捕食模型,证明了系统的解一致有界,并得到了系统一致持久的充分条件.     

Positive Solutions for a Lotka–Volterra Prey–Predator Model with Cross-Diffusion of Fractional Type

In this paper we consider a Lotka–Volterra prey–predator model with cross-diffusion of fractional type. The main purpose is to discuss the existence and nonexistence of positive steady state solutions of such a model. Here a positive solution corresponds to a coexistence state of the model. Firstly we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system. Secondly we derive some necessary conditions to ensure the existence of positive solutions, which demonstrate that if the intrinsic growth rate of the prey is too small or the death rate (or the birth rate) of the predator is too large, the model does not possess positive solutions. Thirdly we study the sufficient conditions to ensure the existence of positive solutions by using degree theory. Finally we characterize the stable/unstable regions of semi-trivial solutions and coexistence regions in parameter plane.     

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values.This paper provides a natural condition of the existence of stable pcsitive steady-state solutions for the one predator two prey system.Under this conditon we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem,discuss the positive stable solution problem bifureated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.     

Dynamics of a Stochastic Predator–Prey Model with Stage Structure for Predator and Holling Type II Functional Response

In this paper, we develop and study a stochastic predator–prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.     

Stationary distribution and extinction of a stochastic predator–prey model with distributed delay

In this paper, we focus on a stochastic predator–prey model with distributed delay. We first obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Then we establish sufficient conditions for extinction of the predator population, that is, the prey population is survival and the predator population is extinct.     

Traveling waves for a reaction–diffusion–advection predator–prey model

In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder’s fixed-point theorem, LaSalle’s invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.     

Periodic solutions in non autonomous predator prey system with delays

In this paper, we consider a biological model for two predators and one prey with periodic delays. By assuming that one predator consumes prey according to Holling II functional response while the other predator consumes prey according to the Beddington–DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions for this model is obtained under suitable conditions.     

Weak-renormalized solutions for predator–prey system

In this article, we consider the predator–prey system with Dirichlet boundary conditions which is used in the modelling of ecology. Under the assumptions of no growth conditions and integrable data, we prove the existence of weak-renormalized solutions to the predator–prey system.     

Dynamics of a predator–prey system with inducible defense and disease in the prey

Establishing and researching a population dynamical model based on the differential equation is of great significance. In this paper, a predator–prey system with inducible defense and disease in the prey is built from biological evolution and Eco-epidemiology. The effect of disease on population stability in the predator–prey system with inducible defense is studied. Firstly, we verify the positivity and uniform boundedness of the solutions of the system. Then the existence and stability of the equilibria are studied. There are no more than nine equilibrium points in the system. We use a sophisticated parameter transformation to study the properties of the coexistence equilibrium points of the system. A sufficient condition is established for the existence of Hopf bifurcation. Numerical simulations are performed to make analytical studies more complete.     

Traveling waves in delayed predator–prey systems with nonlocal diffusion and stage structure

This paper is concerned with the existence of traveling wave solutions of a delayed predator–prey system with stage structure and nonlocal diffusion. By introducing the partial quasi-monotone condition and cross-iteration scheme, we first consider a class of delayed systems with nonlocal diffusion and deduce the existence of traveling wave solutions to the existence of a pair of upper–lower solutions. When the result is applied to the predator–prey system, we establish the existence of traveling wave solutions, as well as its precisely asymptotic behavior. Our result implies that there is a transition zone moving from the steady state with no species to the steady state with the coexistence of both species.     

Dynamics analysis of a reaction–diffusion system with Beddington–DeAngelis functional response and strong Allee effect

In this paper, the dynamics of a diffusive predator–prey model with modified Leslie–Gower term and strong Allee effect on prey under homogeneous Neumann boundary condition is considered. Firstly, we obtain the qualitative properties of the system including the existence of the global positive solution and the local and global asymptotical stability of the constant equilibria. In addition, we investigate a priori estimate and the nonexistence of nonconstant positive steady state solutions. Finally, we establish the existence and local structure of steady state patterns and time-periodic patterns for the system.