一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

Global stability and oscillations in classical Lotka-Volterra loops

The paper considers the classical Volterra system of n ( 3) species in predator-prey relation forming a loop, and derives some global properties of its solutions. Sufficient conditions for global asymptotic stability in terms of parameters are obtained, and also the region of global boundedness in the parameter space is indicated. Lastly a three species system is discussed in detail in relation to its global stability, unboundedness of solutions, existence of periodic and non-periodic oscillations.Work performed under the auspices of G.N.F.M., C.N.R. (Italy) and within the activity of the group Evolution Equations and Applications, M.P.I., (Italy)     

Theoretical Population Dynamics Model of a Genetically Transmitted Disease: Sickle-Cell Anaemia

We formulate a realistic demographic model that captures the pattern of inheritance of the S gene, which is responsible for the most common genetic defect, namely, sickle-cell anaemia (SCA), using general pair formations. The model equation is implicitly solved via the Laplace transform technique, while the existence of a unique solution is proved by applying the contraction mapping principle. One of the main results is the boundedness of the solution. A fundamental reason for the persistence of SCA is probably due to the role played by the selective advantage of the abnormal S gene over the normal haemoglobin A in tropical regions, and the fact that carriers are more fertile and survive longer (a property known as hybrid vigor), because they are essentially asymptomatic. We also discuss possible public health policies. 2000 MS Classification: 92D25 · 92D40 · 34C60 · 35F10     

密度制约竞争二种群Volterra方程解的有界性及参数估计

本文给出密度制约且相互竞争二种群Volterra方程解的一种有界性及存在唯一性的证明。基于此,参考单种群Logistic方程反问题的方法”,给出了该Volterra方程参数的一种估计。     

Global behaviour of age-dependent logistic population models

We study the large time behaviour of a nonlinear population model with a general logistic term. It is proved that every solution must have a limit when time becomes infinite. We present conditions that guarantee the boundedness of the solution. Furthermore, we prove that in general no oscillation is possible for the total number of population. This is in sharp contrast to the linear case.This work was carried out with the aid of a grant from the International Development Centre, Ottawa, Canada     

相互干扰的捕食与被捕食者种群的Hassall模型定性分析

本文证明了Hassall模型的渐近稳定性、有界性、全局稳定性。解决了文献[1]对该模型的三个猜想：（1）模型在某种条件下,正平衡点（x^*,y^*）是渐近稳定的;（2）模型的一切正初始条件的解有界;（3）模型在一定条件下,正平衡点（x^*,y^*）是全局稳定的。     

The role of transmissible diseases in the Holling-Tanner predator-prey model

Transmissible diseases are known to induce remarkable major behavioral changes in predator-prey systems. However, little attention has been paid to model such situations. The latter would allow to predict useful applications in both dynamics and control. Here the Holling-Tanner model is revisited to account for the influence of a transmissible disease, under the assumption that it spreads among the prey species only. We have found the equilibria and analyzed the behavior of the system around each one of them. A threshold result determining when the disease dies out has been identified. We also investigated the parametric space under which the system enters into Hopf and transcritical bifurcations, around the disease free equilibrium. The system is shown to experience neither saddle-node nor pitch-fork bifurcation. Global stability results are obtained by constructing suitable Lyapunov functions.     

Global stability and persistence in LG–Holling type II diseased predator ecosystems

A Leslie–Gower–Holling type II model is modified to introduce a contagious disease in the predator population, assuming that disease cannot propagate to the prey. All the system’s equilibria are determined and the behaviour of the system near them is investigated. The main mathematical issues are global stability and bifurcations for some of the equilibria, together with sufficient conditions for persistence of the ecosystem. Counterintuitive results on the role played by intraspecific competition are highlighted.     

非自治LOTKA-VOLTERRA生态系统的有界性及周期解的存在性

本文利用图论和Liapunov方法研究了非自治LOTKA-VOLTERRA生态系统的有界性和周期解的存在性,得到了一些新的结果．     

具性别偏食的二种群捕食者-食饵系统模型

本文根据生态学实验现象研究了一类二种群捕食者－食饵系统,其中捕食者对食饵有性别偏食情形。建立了相应的数学模型,并对该模型的有关性状进行了分析。