Predator–Prey model with Holling response function of type II and SIS infectious disease

We analyze the influence of a SIS infectious disease affecting Preys or both Predators and Preys in a Predator–Prey model. The response function used here is Holling function type II. Many thresholds are computed and used to investigate the global stability results. The disease can disappear from the community, persist in one or two populations of the community. At least one population can disappear from the community because of disease. In some cases, the model exhibits periodic solutions with persistence of the disease or without disease. Numerical simulations are used with nonstandard numerical schemes to illustrate our results.     

The spreading speed for a predator–prey model with one predator and two preys

We study a predator–prey model with two preys and one predator. Our main concern is the invasion process of the predator into the habitat of two aborigine preys. We consider the case when the two preys are weak competitors in the absence of predator. Under certain conditions, we are able to characterize the asymptotic spreading speed by the parameters of the model.     

具有捕食正效应及Holling Ⅱ功能性反应的捕食-食饵系统

本文研究一类具有捕食正效应的Holling Ⅱ功能性反应的食饵-捕食者系统:dx/dt=rx(1-x/k+εy/k)-αxy/1+ωx,dy/dt=kαxy/1+ωx-dy,讨论其平衡点的性态.     

Steady state in a cross-diffusion predator–prey model with the Beddington–DeAngelis functional response

The purpose of this paper is to study the existence of steady state in a linear cross-diffusion predator–prey model with Beddington–DeAngelis functional response. The proofs mainly rely on Fixed point index theory and analytical techniques.     

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.     

一个具有非线性接触率和种群动力学的传染病模型

本文研究了具有非线性接触率和易感类中具有Ｌｏｇｉｓｔｉｃ增长的ＳＩ传染病模型的正不变集，平衡位置以及平衡位置的稳定性。     

A two-fluid storage model with Lévy inputs and alternating outputs

In this paper we consider a storage model with two types of inputs and outputs that are subject to seasonal switching. Inputs are assumed to occur in a fluid fashion whereas outputs occur at a unit rate so long as the corresponding storage is non-empty. The distribution properties of the storage levels {Z ₁(t),Z ₂(t)} are derived at finite time as well as in stationary regime. We first investigate this process embedded at the successive switching points. This process is Markovian with independent components. In continuous time the components {Z ₁(t),Z ₂(t)} are also independent for each finite t, but are dependent in stationary regime.      

Impulsive periodic oscillation for a predator–prey model with Hassell–Varley–Holling functional response

This paper considers impulsive periodic oscillation in a predator–prey model with Hassell–Varley–Holling functional response. Based on classical continuous theorem of coincidence degree and skilful analysis techniques, some sufficient and necessary criteria for the existence of positive periodic solutions are derived, which are used to generate impulsive control strategy to excite or remove the periodic oscillation in this system. We give some numerical examples to illustrate main results and present some interesting problems.     

具时滞的捕食 食饵系统的一致持久性

研究周期环境下具时滞的Volterra Lotka捕食 食饵系统,利用持久性理论,积分均值和微分不等式的方法,建立了关于一致持久的充分必要判别准则。得到新的结果。     

Coexistence and stability of predator-prey model with Beddington-DeAngelis functional response and stage structure

We present a predator-prey model of Beddington-DeAngelis type functional response with stage structure on prey. The constant time delay is the time taken from birth to maturity about the prey. By the uniform persistence theories and monotone dynamic theories, sharp threshold conditions which are both necessary and sufficient for the permanence and extinction of the model as well as the sufficient conditions for the global stability of the coexistence equilibria are obtained. Biologically, it is proved that the variation of prey stage structure can affect the permanence of the system and drive the predator into extinction by changing the prey carrying capacity: Our results suggest that the predator coexists with prey permanently if and only if predator's recruitment rate at the peak of prey abundance is larger than its death rate; and that the predator goes extinct if and only if predator's possible highest recruitment rate is less than or equal to its death rate; furthermore, our results also show that a sufficiently large mutual interference by predators can stabilize the system.     

Turing pattern formation in a predator–prey system with cross diffusion

The paper explores the impacts of cross-diffusion on the formation of spatial patterns in a ratio-dependent predator–prey system with zero-flux boundary conditions. Our results show that under certain conditions, cross-diffusion can trigger the emergence of spatial patterns which is however impossible under the same conditions when cross-diffusion is absent. We give a rigorous proof that the model has at least one spatially heterogenous steady state by means of the Leray–Schauder degree theory. In addition, numerical simulations are performed to visualize the complex spatial patterns.     

The effect of refuge and immigration in a predator–prey system in the presence of a competitor for the prey

This paper considers the effect of immigration and refuge on the dynamics of a three species system in which one predator feeds on one of two competing species. Immigration is assumed only for the species which is not attacked by the predator.The main results address the stability of the system. Namely, it is shown that increasing the number of refuges stabilizes the system, whereas the opposite holds true by increasing the immigration rate. Also, one result about the persistence of the system and one concerning the global stability of the coexistence equilibrium are presented. Some numerical simulations illustrate the obtained results.     

具时滞的捕食-食饵系统的一致持久性

研究周期环境下具时滞的Volterra-Lotka捕食-食饵系统。利用持久性理论，积分均值和微分不等式的方法。建立了关于一致持久的充分必要差别准确。得到新的结果。