基于比率的具有反馈控制的非自治捕食系统的动力学行为

讨论了一类基于比率的具有反馈控制的非自治捕食系统,所有的参数都是时滞的.先研究了该系统的一致持久性和全局渐近稳定性,并通过构造适当的Lyapunov函数,得到了系统存在惟一渐近稳定的正概周期解的充分性条件.最后,通过一个例子说明了结论的可行性.     

具常投放率的反应扩散系统的渐近性质

本文研究一类具常投放率的人口动力学中反应扩散系统的Neumann初边值问题,应用比较函数讨论其解的渐近性态,给出稳态解的存在条件．     

STABLE POSITIVE SOLUTION OF THE NONAUTONOMOUS LOTKA-VOLTERRA MUTUALISTIC SYSTEM

l！ntroductionAutonomousLotka－VolterramutuallstlcsystemhasbeenstudiedInmanypaperE3】,E4］．［5】,ourpurposehereIstoconsiderthenonautonomouStwo－SPPCllsLOtkt－Volterramutuallstlcsystem．WeareconcernedwiththedifferentialequationsbelongtoC‘andC‘isthesetOfsllCOlltlnuouSfunCtionSg：［0,＋。）、RbOUnded。hove。ndbelOWbyCOnst。ms,moreover,notallofa：。（t）（l＜l,j＜n,。／j）arezero．Theper。odlccasehasbeenconsideredIn［1】．Insection3ofthlspaper,westudiedthegeneralcaseoftlmede…     

时变系数Lotka-volterra互惠共存系统正解的全局渐近性

本文就对变系统Lotka-volterra互惠共存系统的渐近系统进行讨论,得到渐近系统（2）的解关于（l）的解的全局渐近性．     

Growth analysis of the self-thinning stands of Pinus densiflora Sieb. et Zucc

The competition-density (C-D) effect for self-thinning Pinus densiflora Sieb. et Zucc. stands was analyzed. The relationship between biological time and physical time t followed a hyperbolic curve. The coefficients A_t and B included in the reciprocal equation of the C-D effect in self-thinning stands (i.e. 1/w=A_t+B), where w and , respectively, represent the mean stem volume and the realized stand density, were calculated at each time. With increasing , the coefficient A_t increased abruptly up to a maximum value, and then decreased gradually to a constant level, whereas the coefficient B decreased exponentially. The relationship between the realized stand density and the initial stand density _i was confirmed to follow the equation: 1/=1/_i+, where 1/ represents the asymptotic stand density at a given time. The - relationship was represented by the equation: =p(e–1), where p and are constants. The density in the self-thinning stands tended to converge to the same density level after a sufficient lapse of time, irrespective of the difference in initial stand density. The time-trajectory of the mean stem volume and asymptotic stand density on logarithmic coordinates moved gradually toward the self-thinning line with a slope of approximately –3/2, whereas the time-trajectory of the mean stem volume and full stand density moved initially along the self-thinning line with a slope of approximately –3/2, and then changed to move along the maximum yield line with a slope of –1.0.     

Lyapunov functions for Lotka–Volterra predator–prey models with optimal foraging behavior

 The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka–Volterra predator–prey systems with optimal foraging behavior. We examine a predator–prey model with alternative food, a two-patch model with mobile predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka–Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous differential equations. Received: 23 March 1999     

Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)

One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models.     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

Comparing trends in cancer rates across overlapping regions

Monitoring and comparing trends in cancer rates across geographic regions or over different time periods have been major tasks of the National Cancer Institute's (NCI) Surveillance, Epidemiology, and End Results (SEER) Program as it profiles healthcare quality as well as decides healthcare resource allocations within a spatial-temporal framework. A fundamental difficulty, however, arises when such comparisons have to be made for regions or time intervals that overlap, for example, comparing the change in trends of mortality rates in a local area (e.g., the mortality rate of breast cancer in California) with a more global level (i.e., the national mortality rate of breast cancer). In view of sparsity of available methodologies, this article develops a simple corrected Z-test that accounts for such overlapping. The performance of the proposed test over the two-sample "pooled"t-test that assumes independence across comparison groups is assessed via the Pitman asymptotic relative efficiency as well as Monte Carlo simulations and applications to the SEER cancer data. The proposed test will be important for the SEER * STAT software, maintained by the NCI, for the analysis of the SEER data.     

非自治阶段结构合作系统的持久性与周期解

本文研究一类非自治阶段结构的合作系统,得到系统的最终有界性,对应周期系统正周期解的存在性,唯一性以及全局渐近稳定性的充分条件。