捕食者与食饵都染病的捕食-被捕食模型分析

建立并分析了一个捕食者和食饵都染病的捕食-被捕食模型,求得了它的非负平衡点.利用Hurwitz判据,用特征根的方法得到了边界平衡点局部渐近稳定的充分条件.进一步利用LaSalle不变性原理获得了正平衡点全局渐近稳定的充分条件.     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时,模型不存在无病平衡点．对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件．     

一类具有离散时滞的多菌株媒介传染病模型的竞争排斥北大核心CSCD

本文建立和研究了一类具有离散时滞的多菌株媒介传染病模型.证明了当基本再生数R_0<1时,无病平衡点是全局渐近稳定的.证明了与具有最大基本再生数对应的菌株占优平衡点是局部渐近稳定的.在一定条件下,证明了菌株i占优平衡点的全局稳定性的,此时竞争排斥原理成立.     

一类比率型功能性反应捕食模型的稳定性分析

研究了一类具有比率型功能性反应的捕食模型,对模型进行了定性和稳定性分析,讨论了模型唯一正平衡点的存在条件,以及模型各个平衡点的性态.得到了各个平衡点全局渐近稳定的充分条件.通过绘制模型的相轨线,分析轨线的走向得到了原点全局渐近稳定的条件,并证明了模型不存在非平凡正周期解的条件,通过构造Lyapunov函数得到了模型的唯一正平衡点是全局渐近稳定的结论.     

一类竞争——合作生态模型平衡点的渐近稳定性

研究一类竞争-合作生态数学模型平衡点的渐近稳定性,得到了一组保证平衡点渐近稳定的充分条件.     

带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型的稳定性

本文首先应用上下解方法讨论一类带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型解的一致有界性和整体存在性,然后通过线性化方法分别给出该模型的半平凡平衡点和正平衡点局部渐近稳定的充分条件,最后应用Lyapunov泛函方法讨论唯一正平衡点的全局渐近稳定性.     

具有染病者输入的离散SIR传染病模型分析

引入相应的概率建立了具有染病者输入的离散SIR传染病模型,确定了决定其动力学性态的阂值.在阈值之下模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的;在阈值之上模型是一致持续的,有唯一的地方病平衡点存在,且地方病平衡点是局部渐近稳定的.     

具有因病死亡且输人为Berverton-Holt函数的离散SIS传染病模型分析

引入相应的概率建立了考虑因病死亡且输入为Berverton-Holt的离散SIS传染病模型,确定了决定其动力性态的阈值,在阈值之下模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的;在阈值之上模型是一致持续的,有唯一的地方病平衡点存在,且可以猜想地方病平衡点是全局渐近稳定的.     

具有标准发生率和因病死亡率的离散SIS传染病模型的全局稳定性分析

主要研究了具有标准发生率和因病死亡率的离散SIS传染病模型的动力学性质,利用构造Lyapunov函数,得到模型无病平衡点和地方性平衡点的全局稳定性,即无病平衡点是全局渐近稳定的当且仅当基本再生数R_0≤1,地方病平衡点是全局渐近稳定的当且仅当R_0>1.     

具有一般发生率的疟疾传播模型的稳定性研究

研究了一类具有一般发生率的疟疾传播模型,得到了模型的平衡点和基本再生数R_0.通过构造Lyapunov函数得到当R_0≤1时,无病平衡点是全局渐近稳定的;当R_01时,正平衡点是全局渐近稳定的.通过例子说明所得的理论结果.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.