一类具有时滞的三种群食物链模型的定性分析及其仿真

在生态系统中,时滞对种群稳定性的影响一直是研究的重点内容之一.考虑了一类具有时滞的三种群食物链模型,利用微分不等式得到了种群的有界性;利用Matlab软件下的Simulink平台,对种群模型进行了数值仿真,得到了不同参数情况下的相空间轨迹,通过分岔图说明时滞对种群模型稳定性的影响.     

基于营养供需动态平衡考虑的种群生物量增长模型

本文在种群实际增长是限制性营养供需动态平衡所导致的结果这一假定下,推导出了一个单种群生物量增长数学模型。该模型在形式上与崔-Lawson模型相一致。但其3个参数的生物学意义与崔-Lawson模型有不同的内涵。该模型概括了崔-Lawson模型所不能概括的一类单种群物量增长方式,并给出了不同类型生物量增长方式与种群自身特征和营养再循环的分解条件的关系。本模型的建立和解释具有直观性。     

一类单种群增长模型正解的振动性

利用一种新的方法研究了一类单种群增长模型—时滞微分方程N(t)=的解关于其正平衡点N=1的振动性,所获结果改进了已有文献中的相关结论。     

关于一类污染治理的单种群模型的数学研究

以脉冲微分方程为基础,建立了一类污染环境中在固定时刻对污染进行治理的具有时滞效应的单种群阶段结构模型.详细研究了该模型的动力学性质,给出了种群灭绝和持续生存的充分条件,并进一步研究了污染治理和时滞效应对种群灭绝的影响.本文具有很强的生物意义,为环境污染治理问题提供了可靠的依据.     

一类三维非线性系统空间周期解的存在性及唯一性

本文研究了一类描述天然林内红松林种群变化的三维非线性教学模型     

植物种群具有常收获率的一类植物-食植者微分模型

讨论植物种群具有常收获率的一类植物－－食植者微分方程模型。分析了此系统当对植物种群的常收获率逐渐增大的过程中，在第一象限内轨线拓扑结构的变化规律，从而获知对植物种群不同程度的常收获率将对食植生态环境所产生影响的程度。     

广义捕食系统无闭轨的几组充分条件

本文对一类广义捕食系统生物种群生态常微模型建立几组无闭轨的充分条件,为开拓涉及该类模型制作参考类作全局制图定性的研究．     

脉冲污染环境中随机远海-近海鱼类交互模型的生存性研究

环境污染已对海岸线海洋渔业产生了巨大的影响,而近-远海区域的鱼类种群交互也深刻的影响着渔业资源的发展.鉴于此,本文研究了一类具有脉冲污染环境的随机近-远海鱼类交互模型,得到了随机绝灭和强持续的阈值条件,结果表明污染物和环境波动对近-远海鱼类种群的生存性具有显著的影响.     

带有Dirac梳的广义Logistic模型及其动力学分析

本文给出了一类种群增长模型——带有Dirac梳的广义Logistic模型,然后对该模型进行了准确的离散化,并分析了离散后模型的动力学。     

一类在污染环境中单种群模型的动力学行为（英文）

在种群的增长率满足广义logistic方程的情况下,建立了在污染环境中一类新的单种群模型,给出了该模型中种群一致持续生存和灭绝的充分条件.这里建立的模型是He和Wang[Appl.Math.Modell.31(2007)2227-2238]中模型的改进.     

Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

The paper presents the study of one prey one predator harvesting model with imprecise biological parameters. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. We identify the equilibrium points of the model and discuss their stabilities. The existence of bionomic equilibrium of the model is discussed. We study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin’s maximum principle. Numerical examples are presented to support the proposed model.     

The Geographic Spread of “El mal de las caderas” in Capybaras (Hydrochaeris hydrochaeris)

The aim of this work is to describe an epidemiological model for a capybara (Hydrochaeris hydrochaeris) population. The model considers a tabanid (“mutuca”) population (Diptera: tabanidae), as a vector for the disease called “mal de las caderas” in Estero del Ibera, Corrientes, Argentina. The study of this problem has ecological and economical importance since the meat and the hide of the capybara can be an exploitation resource. At first, a threshold value is determined as a function of the model parameters, obtaining a critical carrying capacity which determines the disease propagation or eradication. Then as the carrying capacity condition for the disease existence is satisfied, the existence of traveling wave solution is studied. Independent speeds are considered for the susceptible capybaras, the noninfected insect, and the disease. The speed of propagation for this model is obtained as function of model parameters followed by a discussion of strategies for controlling the spread of the disease. N.A. Maidana is a fellowship Fapesp and partially supported by Grant Fapesp (temático).     

Modelling and analysis of impulsive releases of sterile mosquitoes

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.     

捕食者具有阶段结构和基于比率的捕食系统的正周期解

利用重合度理论中的延拓定理,讨论了捕食者具有阶段结构和比率型功能性反应的捕食模型的正周期解的存在性,得到了保证周期解存在的充分条件,推广了已知的相关结果.     

Pair formation models with maturation period

The standard model for pair formation is generalized to include a maturation period. This model in the form of three coupled delay equations is a special case of the general age-structured model for a two-sex population. The exact conditions for the existence of an exponential (persistent) two-sex solution are derived. It is shown that this solution is unique and locally stable. In order to achieve these results the theory of homogeneous differential equations is extended to a class of homogeneous delay equations.     

General population growth models with Allee effects in a random environment

Allee effects on population growth are quite common in nature, usually studied through deterministic models with a specific growth rate function.In order to seek the qualitative behaviour of populations induced by such effects, one should avoid model-specific behaviours. So, we use as a basis a general deterministic model, i.e. a model with a general growth rate function, to which we add the effect on the growth rate of the random fluctuations in environmental conditions. The resulting model is the general stochastic differential equation (SDE) model that we propose here.We consider two possible cases, weak Allee effects and strong Allee effects, which lead to different qualitative behaviours of the model.We will study the model properties for both cases in terms of existence and uniqueness of the solution, extinction and stationary behaviour of the population. The two cases will be compared with each other and with the general density-dependent SDE model without Allee effects.We then consider as an example the particular case of the classic logistic model and an Allee effect version of it.     

三种群互惠模型抛物系统解的整体存在与爆破

研究了三种群互惠模型的抛物系统,用上下解方法研究解的整体存在性与爆破问题,并给出了相应的条件.结果表明当种群自身的竞争强时解整体存在,反之则有可能爆破.     

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour.     

Existence and stability of equilibria in age-structured population dynamics

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.     

Female dominant age-dependent deterministic population dynamics

Summary In this paper the study of a nonlinear deterministic model of an age/sex differentiated population is started with a proof of existence and uniqueness of solution of the governing equation. We also obtain time dependent upper bounds to the male and female populations as well as necessary and sufficient conditions for equilibrium.