捕食者与食饵都染病的捕食-被捕食模型分析

建立并分析了一个捕食者和食饵都染病的捕食-被捕食模型,求得了它的非负平衡点.利用Hurwitz判据,用特征根的方法得到了边界平衡点局部渐近稳定的充分条件.进一步利用LaSalle不变性原理获得了正平衡点全局渐近稳定的充分条件.     

一类食饵具有不育控制的捕食模型

讨论了一类食饵具有不育控制的两种群捕食模型,得到了系统平衡点的存在条件,证明了平衡点的局部渐近稳定性和全局稳定性,最后给出了全局稳定的数值模拟,以及对参数进行了分析讨论.     

一类具有线性收获率的生物捕食系统的定性分析

对一类两种群均有线性收获率的具HollingII类功能反应的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,得到此类生物捕食系统的平衡点的性态和极限环的存在,不存在的条件,从而对更具一般性的一类具有非常数收获率的食饵-捕食系统作了较为全面的定性分析,补充完善了前人的结果.     

具有食饵避难的Leslie-Gower最优税收模型分析

建立了发生食饵避难的Leslie-Gower捕食与被捕食系统模型,考虑对捕食种群进行有选择捕获.通过控制税收量加以管理来保护渔业资源不被过渡开发,且讨论了系统平衡点的存在性和稳定性,运用Pontryagin最大值原理得到了达到最优税收量的最优平衡解.     

疾病在食饵中传播的具有时滞的捕食被捕食模型的分析

研究了一个疾病在食饵中传播的捕食与被捕食模型.在未引入时滞时,利用Routh-Hurwitz定理证明了正平衡点的局部渐近稳定性.在引入时滞后,主要讨论了正平衡点的稳定性,得到了当经过一系列临界条件时发生Hopf分支.     

一类具收获率的功能性反应自抑制三种群模型定性分析

研究了一类具收获率的功能性反应自抑制三种群捕食模型,运用微分方程稳定性理论,确定了捕食系统模型的平衡点存在的条件和性态,得到了系统正平衡点渐近稳定条件,并且分析了平衡点的全局稳定性及系统持续生存的条件.最后利用Matlab软件进行了数值模拟验证.     

一类生物捕食系统的定性分析

对一类两种群均有收获率的具较为特殊的功能反应函数的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,此类生物捕食系统平衡点的性态和极限环的存在,不存在及唯一的条件,获得了一类食饵-捕食系统的定性分析结果.     

食饵种群受毒素影响的三种群模型的最优收获问题

讨论了在毒素存在的情况下收获食饵的食饵—捕食模型的平衡点稳定性,生物经济平衡点的存在性和最优收获问题,利用Pontryagin极大值原理确定了最优收获策略.     

具有非线性收获及食饵避难的Leslie-Gower模型的税收分析

研究了具有非线性收获及食饵避难的Leslie-Gower模型,讨论了该模型解的正性、有界性及正平衡点的存在性.通过分析特征方程并运用Routh-Hurwitz判别法,得出正平衡点局部渐近稳定的充分性条件.借助Lyapunov函数以及LaSalle不变原理,研究了正平衡点的全局稳定性.利用Pontryagin最大值原理,得到了最优税收τoptimal以及最优平衡解(xoptimal,yoptimal,Eoptimal).数值模拟与理论结果一致.     

一类两种群均有收获率的HollingⅡ类生物捕食系统的定性分析

对一类两种群均有收获率的具HollingⅡ类功能反应的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,得到此类生物捕食系统平衡点的性态和极限环的存在,不存在的条件及开发研究的结论,补充和完善了前人的结果.     

疾病在食饵中流行的捕食与被捕食模型的分析

分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.     

一类疾病在食饵中传播的生态-传染病模型分析

分析并建立疾病在食饵中传播的生态-传染病模型,且考虑易感食饵具有常数输入,捕食者种群以Logistic模型增长,讨论了系统解的有界性和各平衡点的存在性,以及局部渐近稳定性,通过构造适当的Lyapunov函数分析了各平衡点的全局渐近稳定性,并运用比较定理证明了系统的持久性.     

一类具有Allee影响的捕食与被捕食模型

分析并建立了具有Allee影响的捕食与被捕食模型,被捕食者由于自身繁殖或是被捕食而具有了Allee效应,分别讨论了强Allee和弱Allee对被捕食种群的影响,讨论了解的有界性和各平衡点的存在性,并证明了各平衡点的局部渐近稳定性,进一步通过构造适当的Lyapunov函数分析了正平衡点E*的全局渐近稳定性.     

Modeling and stability analysis of a microalgal pond with nitrification

Microalgae culture fed with ammonium may face the presence of nitrifying bacteria. The aim of this paper is to propose and analyze a nonlinear system which represents the dynamics of these two species (microalgae and nitrifying bacteria) in competition for nitrogen (present as ammonium and nitrate produced by nitrification) in a continuous process. The existence and local stability of system equilibria is studied. Reduction by conservation principle, perturbed systems and Lyapunov methods are used to provide sufficient conditions for the global asymptotic stability of the system equilibria. Finally, we illustrate our analysis with a case study, showing which operating conditions (dilution rate and pond depth) can promote the presence of nitrifiers with microalgae.     

A ratio‐dependent predator–prey model with stage structure and optimal harvesting policy

In this paper, a ratio‐dependent predator–prey model with stage structure and harvesting is investigated. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence and stability are performed. By constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. The existence possibilities of bioeconomic equilibria have been examined. An optimal harvesting policy is also given by using Pontryagin's maximal principle. Copyright © 2007 John Wiley & Sons, Ltd.     

An SIRS model with a nonlinear incidence rate

The global dynamics of an SIRS model with a nonlinear incidence rate is investigated. We establish a threshold for a disease to be extinct or endemic, analyze the existence and asymptotic stability of equilibria, and verify the existence of bistable states, i.e., a stable disease free equilibrium and a stable endemic equilibrium or a stable limit cycle. In particular, we find that the model admits stability switches as a parameter changes. We also investigate the backward bifurcation, the Hopf bifurcation and Bogdanov–Takens bifurcation and obtain the Hopf bifurcation criteria and Bogdanov–Takens bifurcation curves, which are important for making strategies for controlling a disease.     

An SIRS model with a nonlinear incidence rate

The global dynamics of an SIRS model with a nonlinear incidence rate is investigated. We establish a threshold for a disease to be extinct or endemic, analyze the existence and asymptotic stability of equilibria, and verify the existence of bistable states, i.e., a stable disease free equilibrium and a stable endemic equilibrium or a stable limit cycle. In particular, we find that the model admits stability switches as a parameter changes. We also investigate the backward bifurcation, the Hopf bifurcation and Bogdanov–Takens bifurcation and obtain the Hopf bifurcation criteria and Bogdanov–Takens bifurcation curves, which are important for making strategies for controlling a disease.     

Existence of equilibria in a decentralized two-level supply chain

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.