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Global Stability of a Predator-Prey System with stage structure for the Predator

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Acta Mathematica Sinica,English Series 2004年第1期20卷 63-70页

作者： YanNiXIAO LanSunCHEN DepartmentofmathematicalSciences TheUniversityofLiverpoolLiverpoolL697ZLUK AcademyofMathematics&SystemSciences ChineseAcademyofScienceBeijing100080.P.R.china

In this paper, some feasibly suffcient conditions are obtained for the global asymptotic stability of a positive steady state of a predator-prey system with stage structure for the predator by using the theory of comp... 详细信息

关键词： Global stability Predator-prey system Competitive systems stage structure

Bistability of a two-species competition model with stage structure

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International Journal of Biomathematics 2021年第2期14卷 41-57页

作者： Xizhuang Xie School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026P.R.China School of Mathematical Sciences Huaqiao UniversityQuanzhouFujian 362021P.R.China

In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

关键词： Bistability Lotka Volterra competition stage structure monotone semiflow

Optimal harvesting strategy and stability analysis of a delay-induced prey-predator system with stage structure

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Journal of Control and Decision 2016年第3期3卷 197-210页

作者： Lingling Xie Jianguo Gao Minghui Yang School of Mathematics and Information Science Beifang University of NationalitiesYinchuanP.R.China

A stage-structured prey-predator model with time delay and harvesting is considered.Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria.Moreover,the existence of a Hopf bifurcation at the coexistence equilibrium is established.Finally,the optimal harvesting problem is formulated and solved by Pontryagin’s maximum principle,and an example is given for illustration.

关键词： stage structure time delay Hopf bifurcation optimal harvesting

Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey

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International Journal of Biomathematics 2021年第4期14卷 85-120页

作者： Qun Liu Daqing Jiang Tasawar Hayat School of Mathematics and Statistics Key Laboratory of Applied Statistics of MOE Northeast Normal University Changchun 130024 Jilin ProvinceP.R.China College of Science China University of Petroleum Qingdao 266580Shandong ProvinceP.R.China Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group King A bdulaziz University JeddahSaudi Arabia

In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.

关键词： Stochastic predator-prey model stage structure distributed delay periodic solution positive recurrence

Periodic Solutions of a Delayed Predator-Prey Model with stage structure for Prey

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Acta Mathematicae Applicatae Sinica 2004年第2期20卷 323-332页

作者： RuiXu Lan-sunChent Fei-longHao DepartmentofMathematics InstituteofShijiazhuangMechanicalEngineeringShijiazhuang050003China AcademyofMathematicsandSystemsScience CASBeijing100080China

A periodic predator-prey model with stage structure for prey and time delays due to negative feed-back and gestation of predator is proposed.By using Gaines and Mawhin's continuation theorem of coincidencedegree theory,sufficient conditions are derived for the existence of positive periodic solutions to the proposedmodel.Numerical simulations are presented to illustrate the feasibility of our main result.

关键词： stage structure predator-prey model time delay periodic solution

Optimal Harvesting and Stability for a Predator-prey System with stage structure

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 423-430页

作者： Xin-yu Song, Lan-sun ChenDepartment of Mathematics. Xinyang Teachers College, Henan 464000, ChinaInstitute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing100080, China Department of Mathematics Xinyang Teachers College Henan China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.

关键词： Optimal harvesting stage structure predator-prey system global asymptotic stability

An SIS Epidemic Model with stage structure and a Delay

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 607-618页

作者： Yan-ni Xiao, Lan-sun ChenAcademy of Mathematics and System Sciences, Chinese Academy of Sciences. Beijing 100080. China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.

关键词： SIS epidemic model threshold globally asymptotically stable hopf bifurcation stage structure

PERIODIC SOLUTION TO A DELAYED PREDATOR-PREY SYSTEM WITH stage structure AND DISPERSION

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Annals of Differential Equations 2011年第1期27卷 28-35页

作者： Yanwei Liu1,Xia Liu2,Lishun Ren1(1. Dept. of Math.,Zhoukou Normal University,Zhoukou 466001,Henan 2. Dept. of Math.,Henan Normal University,Xinxiang 453007,Henan)

In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.

关键词： time delay diffiusion periodic solution stage structure

PERIODIC SOLUTION AND ALMOST PERIODIC SOLUTION OF NONAUTONOMOUS COMPETITIVE MODEL WITH stage structure AND HARVESTING

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Annals of Differential Equations 2005年第1期21卷 73-80页

作者： YaoZhijian Dept.ofMath.andPhysics AnhuiInstituteofArchitectureandIndustryHefei280022

In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution an... 详细信息

关键词： stage structure harvesting uniform persistence global attractivity almost periodic solution