具Monod-Haldane功能反应的四种群食饵-捕食脉冲系统的动力学分析

基于害虫综合管理策略,本文利用脉冲比较定理、Floquent理论及微小扰动法,研究了一类具有Monod-Haldane功能反应、脉冲比例收获和脉冲常数投放的四种群食饵–捕食系统的动力学性质,证明了系统两食饵灭绝和持续生存的充分条件,而且给出了一食饵种群灭绝其余三种群持续生存的两个充分条件。数值模拟表明,随着投放量的增加,系统出现拟周期分支、倍周期分支、混沌、半周期分支等复杂的动力学性质。     

带有Beddington-DeAngelis功能反应、脉冲、连续时滞和广义扩散函数的捕食者-食饵系统的定性分析

本文定性分析了具有Beddington-DeAngelis功能反应、脉冲、连续时滞和广义扩散函数的捕食者-食饵系统.利用脉冲微分方程的比较原理给出了系统持续生存的条件,并使用不动点理论证明了正周期解的存在性,进而给出了系统存在正周期解的充分条件.最后通过构造Lyapunov泛函证明了系统周期解的全局渐近稳定性.该结论可...     

一类具收获的捕食者-食饵系统的周期解分枝与浑沌现象

研究了一类食饵种群具有常数收获率的捕食者-食饵生态系统的周期激励模型，应用Melnikov方法，给出了该系统存在浑沌与次谐分枝的某些条件。     

一个捕食者染病、食饵具有阶段结构的生态 - 流行病模型的稳定性

研究了一个捕食者染病且食饵具有阶段结构的生态 - 流行病模型的稳定性,考虑了捕食者对食饵的 Holling-II 型功能性反应函数,并讨论了由捕食者的妊娠期引起的时滞对模型稳定性的影响。通过计算特征方程的特征值,运用 Hurwitz 判定定理,得到了该模型的在平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点的局部稳定性,得到了正平衡点处存在 Hopf 分支的充分条件。通过构造 Lyapunov 泛函,运用 LaSall 不变集原理得到了该模型的平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点全局稳定的充分条件。     

具有相互干扰的一个捕食者两个食饵系统的综合害虫治理（英文）

考虑到固定时刻化学控制、生物控制及捕食者有相互干扰等因素的影响,本文构建了一个具有生物控制、化学控制及捕食者有干扰影响的三种群捕食-食饵系统.利用脉冲微分理论、小振幅扰动理论和弗洛凯理论,研究了该系统有关食饵灭绝周期解的存在性和全局渐进稳定性等性质.利用比较定理,通过构造适当的李雅普诺夫函数,讨论得到系统持续生存的充分条件.然后通过举例并进行数值模拟进一步讨论了系统复杂的动力学性质.最后分析讨论了所得结果的生物意义并从害虫综合控制角度给出了一些合理的意见与建议.     

一个具有时滞和阶段结构的捕食模型的全局稳定性北大核心CSCD

本文研究了一个比率依赖的、捕食者和食饵均具有阶段结构的捕食者-食饵相互作用模型,并讨论了由捕食者种群的孕期所引起的时滞对种群动力学性态的影响.通过分析相应的特征方程,运用Hurwitz判定定理,文中分别给出了该模型的非负边界平衡点和正平衡点局部稳定的充分条件,并得到了Hopf分支存在的充分条件;运用单调迭代方法和比较定理,分别给出了该模型的非负边界平衡点和正平衡点的全局稳定的充分条件,从而得到了保证该生态系统永久持续生存或灭绝的充分条件.     

一类具Holling Ⅱ型功能性反应的捕食者-食饵系统非平凡周期解的存在性

本文利用Mawhin重合度理论中的延拓定理研究了具HollingⅡ型功能性反应的捕食者—食饵系统非平凡周期解的存在性,得到了更为一般的结果。     

余弦-高斯激光脉冲在单模光纤中的色散效应

首次提出了余弦-高斯激光脉冲,并证明了该脉冲可由两个相位相反的线性啁啾的高斯激光脉冲叠加得到。由NLS方程出发,对余弦-高斯激光脉冲在色散介质中的色散效应进行了详细的研究。研究结果表明,初始啁啾并不影响入射场的光强分布;当脉冲参数a=1.13时,余弦-高斯激光脉冲的初始脉宽有最小值,且比高斯激光脉冲的初始脉宽要窄;余弦-高斯激光脉冲的展宽因子与传输距离、色散长度LD、激光脉冲参数a、初始啁啾参量C和β2的符号有关,余弦-高斯激光脉冲都比高斯激光脉冲的展宽要快,且参数a越大展宽就越明显。     

线性脉冲微分方程初值问题的ω-周期解(英文)北大核心CSCD

本文利用广义常微分方程理论,得到了线性脉冲微分方程的通解公式,并利用ω-周期解的定义和线性代数方程的性质,得到了线性脉冲微分方程初值问题的ω-周期解.     

具有脉冲效应的Holling—Tanner捕食-被捕食系统的正周期解

为了描述突然性因素对捕食一被捕食系统的影响,本文建立了具有固定时刻脉冲影响的Holling-Tanner捕食-被捕食系统模型,研究了系统的正周期解的存在性.利用基于叠合度理论的连续定理,证明了模型的正T-周期解的存在性,给出了系统存在正周期解的条件,该条件由两个种群的内禀增长率、脉冲周期及一个脉冲周期内的脉冲影响总量给出,这说明脉冲影响可能导致种群系统的平衡状态发生改变.     

Effect of cannibalism on a predator–prey system with nutritional value: a model based study

Enrichment of a simple predator–prey system results in the destruction of stable steady state and further enrichment leads to the extinction of the species, which is a classical problem in ecology and known as the paradox of enrichment. The Paradox of enrichment is a controversial issue. Most theoretical studies show the destabilization of predator–prey system due to enrichment, but there is a discrepancy between the empirical evidence and theoretical predictions. In spite of the debate and cross-debate, research is still being carried out on the paradox of enrichment (16 papers and nearly 500 citations in 2008), which in general does not include the effect of cannibalism. Here we present a simple predator–prey system in the presence of cannibalism among predators and offer a novel resolution to the paradox of enrichment. The concept of nutritional value is introduced by many authors to resolve the issue. It is observed that even in the face of sufficient enrichment the system remains stable in the vicinity of critical nutritional value. In the case of a lower cannibalism rate we also observe similar kinds of behaviour, but for a higher cannibalism rate, the system remains always stable and does not depend upon the nutritional value of prey, i.e. paradox of enrichment does not hold at all in such a situation. We also observe that cannibalism can have a positive as well as a negative effect on population abundance, depending on the cannibalism rate.     

Age-structured predator–prey model with habitat complexity: oscillations and control

In this article, we study a predator–prey interaction in a homogeneously complex habitat where predator takes a fixed time to develop from immature to its mature stage. The age-structure of the predator and its interaction with the prey is framed in a system of delay differential equations. The objective is to study the role of habitat complexity and the maturation delay of the predator on the overall dynamics of the model system. Different interesting dynamical behaviours can be obtained by regulating two key parameters, namely the degree of habitat complexity and the maturation delay. It is observed that the system becomes unstable from its stable condition when the maturation delay crosses some critical value. The periodic solutions bifurcated from the interior equilibrium is found to be supercritical and stable. Synchronization of population fluctuations is, however, possible by increasing the strength of habitat complexity. The predator population goes to extinction and the prey population reaches to its maximum, irrespective of the length of maturation delay, when the habitat complexity crosses some upper critical value. The qualitative dynamical behaviours of the model system are verified with the data of Paramecium aurelia (prey) and Didinium nasutum (predator) interaction.     

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.     

一类食饵中存在疾病的捕食系统的SIS传染病模型

研究了一类疾病只在食饵中存在的捕食系统的SIS传染病模型.在此模型中,不考虑疾病对捕获率的影响.通过理论分析,给出了各类平衡点全局渐近稳定性的条件,揭示了捕食因素对疾病传播的影响.所得结论表明,捕食者的引入,将会使原来的单种群传染病模型的稳定性态无论是定量上还是定性上都将产生变化.     

Predator confusion is sufficient to evolve swarming behaviour

Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator–prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator–prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behaviour in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator''s visual field, favouring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator''s consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint—predator confusion—could have pervasive evolutionary effects on prey behaviour, predator sensory mechanisms and the ecological interactions between predators and prey.     

Hydrodynamics of prey capture in sharks: effects of substrate

In suction feeding, a volume of water is drawn into the mouth of a predator. Previous studies of suction feeding in fishes have shown that significant fluid velocities are confined to a region within one mouth width from the mouth. Therefore, the predator must be relatively close to the prey to ensure capture success. Here, theoretical modelling is combined with empirical data to unravel the mechanism behind feeding on a substrate. First, we approached the problem theoretically by combining the stream functions of two sinks. Computational fluid dynamics modelling is then applied to make quantitative predictions regarding the effects of substrate proximity on the feeding hydrodynamics of a benthic shark. An oblique circular cylinder and a shark head model were used. To test the models, we used digital particle image velocimetry to record fluid flow around the mouth of white-spotted bamboo sharks, Chiloscyllium plagiosum, during suction feeding on the substrate and in the water column. Empirical results confirmed the modelling predictions: the length of the flow field can be doubled due to passive substrate effects during prey capture. Feeding near a substrate extends the distance over which suction is effective and a predator strike can be effective further from the prey.     

A minimal model of predator–swarm interactions

We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a ‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, the predator is able to catch up with the swarm as a whole, but the individual prey is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become chaotic. For even higher strength, the predator is able to successfully capture the prey. Our model is simple enough to be amenable to a full mathematical analysis, which is used to predict the shape of the swarm as well as the resulting predator–prey dynamics as a function of model parameters. We show that, as the predator strength is increased, there is a transition (owing to a Hopf bifurcation) from confusion state to chasing dynamics, and we compute the threshold analytically. Our analysis indicates that the swarming behaviour is not helpful in avoiding the predator, suggesting that there are other reasons why the species may swarm. The complex shape of the swarm in our model during the chasing dynamics is similar to the shape of a flock of sheep avoiding a shepherd.     

Prey should hide more randomly when a predator attacks more persistently

When being searched for and then (if found) pursued by a predator, a prey animal has a choice between choosing very randomly among hiding locations so as to be hard to find or alternatively choosing a location from which it is more likely to successfully flee if found. That is, the prey can choose to be hard to find or hard to catch, if found. In our model, capture of prey requires both finding it and successfully pursuing it. We model this dilemma as a zero-sum repeated game between predator and prey, with the eventual capture probability as the pay-off to the predator. We find that the more random hiding strategy is better when the chances of repeated pursuit, which are known to be related to area topography, are high. Our results extend earlier results of Gal and Casas, where there was at most only a single pursuit. In that model, hiding randomly was preferred by the prey when the predator has only a few looks. Thus, our new multistage model shows that the effect of more potential looks is opposite. Our results can be viewed as a generalization of search games to the repeated game context and are in accordance with observed escape behaviour of different animals.     

A Two-Patch Predator-Prey Metapopulation Model

A minimal model for predator-prey interaction in a composite environment is presented and analysed. We first consider free migrations between two patches for both interacting populations, and then the particular cases where only one-directional migration is allowed and where only one of the two populations can migrate. Our findings indicate that in all cases the ecosystem can never disappear entirely, under the model assumptions. The predator-free equilibrium and the coexistence of all populations are found to be the only feasible stable equilibria. When there are only one-directional migrations, the abandoned patch cannot be repopulated. Other equilibria then arise, with only prey in the second patch, coexistence in the second patch, or prey in both patches but predators only in the second one. For the case of sedentary prey, with predator migration, the prey cannot thrive alone in either of the two environments. However, predators can survive in a prey-free patch due to their ability to migrate into the other patch, provided prey is present there. If only the prey can migrate, the predators may be eliminated from one patch or from both. In the first case, the patch where there are no predators acts as a refuge for the survival of the prey.