Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-Ⅳ Functional Response

In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳfunctionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.     

Bifurcations and Chaos in Duffing Equation

The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcingis investigated.The conditions of existence of primary resonance,second-order,third-order subharmonics,m-order subharmonics and chaos are given by using the second-averaging method,the Melnikov method andbifurcation theory.Numerical simulations including bifurcation diagram,bifurcation surfaces and phase portraitsshow the consistence with the theoretical analysis.The numerical results also exhibit new dynamical behaviorsincluding onset of chaos,chaos suddenly disappearing to periodic orbit,cascades of inverse period-doublingbifurcations,period-doubling bifurcation,symmetry period-doubling bifurcations of period-3 orbit,symmetry-breaking of periodic orbits,interleaving occurrence of chaotic behaviors and period-one orbit,a great abundanceof periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaoticattractors.Our results show that many dynamical behaviors are strictly departure from the behaviors of theDuffing equation with odd-nonlinear restoring force.     

具时滞带非单调反应函数的半比例依赖捕食被捕食系统的持久性

研究了具时滞半比例依赖的捕食被捕食非单调函数反应系统的持久性,得到了比较弱的由积分形式表述的充分条件.     

捕食者-被捕者中含有化学计量学的离散型模型

大部分捕食者-被捕者模型是连续的,但是生物的发展未必是连续的,而且环境变化对生物的作用普遍存在时滞性.根据连续系统考虑的捕食者和被捕者的相互作用、Beverton-Holt差分方程以及化学计量学因素对系统的影响,建立了离散的捕食者-被捕者模型.分析表明:新建立的模型,基本上保留了连续系统的基本特征,揭示了能量富足的矛盾.进一步通过对全局的吸引集的构造,对模型的动力学行为有深刻的认识,还指出了生物灭绝和濒临灭绝的差别,这表明新模型比连续系统和直接利用连续解的离散方法得到的离散模型包含更多的生物意义.     

具有功能性反应函数为的捕食系统

本文给出了具有功能性反应函数为 x的捕食系统x=γx-δ x y-αx2 ,y=-sy+β x y-εy2的全局相图 .得到了两种群持续共存和捕食者种群必将灭绝的条件 .讨论了此系统唯一正平衡点的 Hopf分支 ,并证明了该点可以成为二阶不稳定细焦点 ,从而得到该系统有出现至少三个极限环的可能 .     

离散Hassell-Varley型功能性反应系统的正周期解

研究具有Hassell-Varley型功能性反应的捕食者—食饵系统并建立了非自治差分方程模型.利用新的解的估计技巧,并运用拓扑度的同伦不变性,得到了这类系统正周期解存在的充要条件.     

一类具有HollingⅢ型食饵—捕食系统的周期解存在性

利用重合度理论中的延拓定理研究非自治周期食饵—捕食系统的非平凡周期解存在性,给出了周期解存在的充分条件.     

一类具有Watt型功能性反应的捕食系统的极限环与稳定性

研究一类具有Watt型功能性反应的捕食模型.讨论了该系统正平衡点的存在性以及非负平衡点的性态,应用Poincare-Bendixson定理和张芷芬定理,证明了极限环的存在性和唯一性,并采用构造Dulac函数的方法,获得了正平衡点全局渐近稳定性的一个充分条件.     

一类具Holling-IV的捕食-食饵系统的Hopf分岔

研究了具有简化Holling-IV功能反应函数捕食-食饵模型二阶细焦点的Hopf分岔问题.运用隐函数存在定理,证明了该模型二阶细焦点确定的系数经扰动后在其邻域内有二个极限环.     

一类具脉冲效应和单调功能反应的时滞捕食系统的正周期解

利用重合度理论中的延拓定理,获得了一类具有脉冲效应和单调功能反应的时滞捕食系统正周期解存在性的充分条件.最后,通过列举三个例子表示我们等待结果的有效性.     

具有阶段结构和时滞的捕食系统

§ 1　IntroductionThe competitive,cooperative and predator-prey models have been studied by many au-thors.[1— 4] The permanence (or strong persistence) and extinction are significant conceptsof those models.However,the stage structure of species has been considered very little.Inthe real world,almost all animals have the stage structure of immature and mature.Re-cently,papers[5— 7] studied the stage structure of species,the transformation rate of ma-ture population is proportional to the ex…     

一类具有HollingⅠ型功能反映的半比例依赖捕食-食饵离散系统的持久性

主要研究了一类具有Holling I型功能函数半比例依赖的捕食-食饵离散系统的一般非自治情形,得到了系统的持久性的充分条件.     

Non-Constant Positive Steady States of a Predator-Prey System with Non-Monotonic Functional Response and Diffusion

This paper deals with non-constant positive steady-state solutionsof a predator-prey system with non-monotonic functional response,also called Holling type-IV interaction terms, and diffusionunder the homogeneous Neumann boundary condition. We first establishpositive upper and lower bounds for such solutions, and thenstudy their non-existence, global existence and bifurcation.2000 Mathematics Subject Classification 35J55, 92D25.     

Bogdanov-Takens bifurcation in a Leslie-Gower predator-prey model with prey harvesting

This paper discuss the cusp bifurcation of codimension 2 （i.e. Bogdanov-Takens bifurcation） in a Leslie~Gower predator-prey model with prey harvesting, which was not revealed by Zhu and Lan [Phase portraits, Hopf bifurcation and limit cycles of Leslie-Gower predator-prey systems with harvesting rates, Discrete and Continuous Dynamical Systems Series B. 14（1） （2010）, 289-306]. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop.     

一类稀疏效应下具功能反应的捕食系统的定性分析

对稀疏效应下具有Holling Ⅲ类功能反应的一类捕食系统进行了定性分析,讨论了正平衡点的存在性和稳定性,并通过分析参数的取值范围得到了极限环、分界线环的存在条件与相关稳定性的结论.     

具有HollingIV类功能性反应时滞扩散捕食模型的多个周期解

考虑一类具有HollingIV类功能性反应时滞扩散捕食模型.该模型的系数为周期函数,这和环境的周期变化相一致.作者应用重合度定理,建立了该模型具有至少两个正周期解的充分条件.     

一类具有功能性反应的中立型捕食者-食饵系统全局正周期解的存在性

首次研究一类具有HollingⅡ型功能性反应中立型捕食者-食饵系统(即Rosenzweig- MacArthur模型),通过发展一些分析技巧,利用重合度理论中的延拓定理讨论了其全局正周 期解的存在性,得到了保证周期解存在的充分条件．最后举例说明该文定理条件是可行的．     

Bifurcations and Stability Boundary of a Power System

A single-axis flux decay model including an excitation control model proposed in [12,14,16] isstudied.As the bifurcation parameter P_m (input power to the generator) varies,the system exhibits dynamicsemerging from static and dynamic bifurcations which link with system collapse.We show that the equilibriumpoint of the system undergoes three bifurcations:one saddle-node bifurcation and two Hopf bifurcations.Thestate variables dominating system collapse are different for different critical points,and the excitative controlmay play an important role in delaying system from collapsing.Simulations are presented to illustrate thedynamical behavior associated with the power system stability and collapse.Moreover,by computing the localquadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point,an analytical expressionfor the approximate stability boundary is worked out.     

周期时间制约的非Hamliton可积Kolmogorov系统的混沌与次谐波

本文研究一类非Hamilton可积的Kolmogorov生态系统的周期激励模型，应用Melnikov方法，得到了该系统存在混沌与次谐分枝的某些充分条件。     

一类具脉冲效应的三种群捕食系统的动力学性质

基于综合害虫管理,提出并研究了一类具有脉冲效应和Holling Ⅱ类功能反应的两个捕食者一个食饵系统.利用脉冲微分方程的Floquet理论和比较定理,得到了系统灭绝和持续生存的充分条件.最后,简要讨论了该综合害虫管理策略的有效性及系统在周期脉冲扰动下的动力复杂性.