具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为北大核心CSCD

该文研究了一类具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为,证明了系统全局正解的存在性和唯一性,得到了灭绝性和持久性的充分条件.在此基础上,给出了控制捕食-食饵系统随机持久和灭绝的阈值,并且讨论了系统解的一些渐近性态.最后通过数值模拟,验证了结果的有效性.     

具阶段结构的非自治捕食模型的持久性

讨论了一类具有密度制约且食饵带有阶段结构和捕食者仅捕食成年食饵的捕食-食饵种群模型,,得到了持久生存以及非平凡周期解存在的充分条件.     

一类捕食者具有阶段结构的捕食——被捕食模型的全局性态分析

在假设捕食的受益是减少死亡下,建立了一类捕食种群具有阶段结构的捕食-被捕食模型,分析得到了不存在食饵种群情形下捕食者种群模型和食饵存在时捕食-被捕食模型的平衡点存在性和全局稳定性,并确定了决定模型动力学性态的捕食者种群基本再生数、捕食存在时的食饵种群净增长率以及食饵灭绝与否的捕食率阈值.     

具有反馈控制和Beddington-DeAngelis功能性反应的非自治扩散模型的概周期解

讨论了一类具有反馈控制和B edd ington-D eA ngelis功能性反应的非自治捕食-食饵扩散模型,其中食饵可以在两个斑块有限制地扩散,但对捕食者来说,斑块间的扩散不受限制.本文结合运用Lyapunov函数,得到该模型存在唯一的全局渐进稳定的正概周期解的条件.     

食饵具有避难所效应的生态-传染病模型的分析

建立并分析了疾病在食饵中传播、食饵考虑避难所效应的捕食与被捕食模型,捕食者不仅捕食感染食饵而且捕食易感食饵.讨论了系统的有界性和各平衡点的存在性,利用Routh-Hurwitz判据分析各平衡点的局部渐进稳定性,通过构造Lyapunov函数证明了各平衡点的全局渐进稳定性,并进行数值模拟以验证结论的正确性.     

食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支

研究一类食饵具庇护所的基于比率捕食-食饵模型,得到该模型的全局稳定、极限环以及Hopf分支等的一系列充分条件.研究表明当模型捕食种群转化率、死亡率和半饱和常数满足一定条件时,食饵庇护量不影响捕食、食饵两种群的共存.一旦该条件不满足,则食饵庇护量具有稳定化作用.数值模拟验证了所得结论的可行性.     

带有脉冲和Holling-Ⅳ型功能反应函数的中立型捕食-食饵模型的周期解

该文研究一类带有中立型脉冲时滞和Holling-Ⅳ型功能反应函数的捕食-食饵模型.通过运用Mawhin迭合度理论和分析技巧,得到了捕食-食饵模型正周期解存在性的充分条件.     

一类具有分段常数变量的三维食饵捕食者系统的稳定性和分支行为

本文研究一类具有分段常数变量的三维食饵-捕食者系统的稳定性和分支行为,该系统由一个捕食者和两个食饵构成,其中一个食饵可由捕食者对另一个食饵的捕食行为中获益.首先通过计算得到三维食饵-捕食者系统对应的差分模型,其次通过选择合适的参数讨论边界和正平衡点的存在性,进而利用线性稳定性理论讨论平衡点局部渐近稳定的充分条件.将两个食饵种群的出生率以及最大环境容纳量作为分支参数,使用分支理论研究差分模型在平衡点处产生翻转分支、Neimark-Sacker分支、折-翻转分支和1:2共振分支的充分条件.最后通过数值模拟验证了理论分析的正确性.     

具有二次自作用的捕食-食饵系统的动力学分析

本文研究一个具有二次自作用的随机捕食-食饵系统,给出其种群随机灭绝、随机持久的充分条件.     

具有时滞和扩散的随机捕食-食饵系统

该文建立一个具有时滞和食饵扩散的随机捕食-食饵模型.首先,确定系统对任何正初始值存在唯一全局正解;其次,给出了种群灭绝与平均持续生存的条件;最后,给出数值例子支撑该文的结论.     

Analysis of a predator-prey model with Crowley-Martin and modified Leslie-Gower schemes with stochastic perturbation

In this paper, we study a nonautonomous predator-prey model with Crowley-Martin and modified Leslie-Gower schemes with stochastic perturbation. The existence of a global positive solution and stochastically ultimate boundedness are obtained. Sufficient conditions are established for extinction, persistence in the mean, and stochastic permanence of the system. Finally, simulations are carried out to verify our results.     

Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

In this paper, we consider a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique positive solution to the system with positive initial value, and mainly investigate the long time behavior of the system. Condition for the system to be extinct is given and persistent condition is established. At last, numerical simulations are carried out to support our results.     

Qualitative analysis of a stochastic ratio-dependent predator-prey system

A stochastic ratio-dependent predator-prey model is investigated in this paper. By the comparison theorem of stochastic equations and Itô’s formula, we obtain the global existence of a positive unique solution of the ratio-dependent model. Besides, a condition for species to be extinct is given and a persistent condition is established. We also conclude that both the prey population and the ratio-dependent function are stable in time average. In the end, numerical simulations are carried out to confirm our findings.     

Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

     

Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise

In this paper, well-posedness and asymptotic behaviors for a predator-prey system with Lévy noise are studied by using stochastic analytical techniques. Firstly, the existence and uniqueness of positive global solution with positive initial value is proved. Then, stochastic permanence for the system is investigated. Finally, persistence in mean and extinction for the system are discussed and some numerical simulations are provided to support our results.     

Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response

In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results.     

一类具有阶段结构的随机捕食与被捕食模型的全局稳定性分析（英文）

In this paper, a stochastic predator-prey model with stage structure for predator and ratio-dependent functional response is concerned. Sufficient conditions for the global asymptotic stability of positive equilibrium are established. Some numerical simulations are carried out to illustrate the theoretical results.     

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.     

Non-constant positive steady-states of a diffusive predator-prey system in homogeneous environment

In this paper, we investigate the existence and non-existence of non-constant positive steady-states of a diffusive predator-prey interaction system under homogeneous Neumann boundary condition. In homogeneous environment, we show that the predator-prey model with Leslie-Gower functional response has no non-constant positive solution, but the system with a general functional response may have at least one non-constant positive steady-state under some conditions.