Statistics of the Occupation Time of Renewal Processes

We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability density functions of these random variables have very different scalings in time. We analyze successively the cases where this distribution is narrow, where it is broad with index <1, and finally where it is broad with index 1<<2. The methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes (see joint paper by G. De Smedt, C. Godrèche, and J. M. Luck⁽²⁶⁾).     

一类三种群第一类功能反应系统分析

摘要本文研究了由两个捕食种群和一个食饵种群组成的第一类功能反应三种群系统的种群幸存和灭绝的状态,并作了生态学方面的讨论。     

On Stability and Persistence of Some Oligopoly Models

A dynamic oligopoly model is given. Its steady state and stability and the bounds of its basin of attraction are studied. Delay (memory) is then introduced. Oligopoly is then reformulated using Smale's game which is more realistic than ordinary games since it takes memory into consideration. Persistence is studied for some oligopoly models.     

THE POSITIVE PERIODIC SOLUTIONS OF PERIODIC RFDEs WITH INFINITE DELAY

This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.     

微生物食物链培养系统的极限性态

本文考虑多种微生扬在一个培养室中混合培养,这些微生物之间是作为食物链而相依相存的,本文假定营养液的浓度及微生物对资源的消耗率等因素都是时间的有界函数,得到了微生物种群生存和绝灭的条件。     

Equilibrium Pure States and Nonequilibrium Chaos

We consider nonequilibrium systems such as the Edwards–Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken-symmetry pure states. Following a deep quench, we argue that as time t, although the system is usually in some pure state locally, either it never settles permanently on a fixed length scale into a single pure state, or it does, but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). We prove that the former case holds for deeply quenched 2D ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages do not necessarily disagree with Boltzmann averages.     

A Continuous Super-Brownian Motion in a Super-Brownian Medium

A continuous super-Brownian motion is constructed in which branching occurs only in the presence of catalysts which evolve themselves as a continuous super-Brownian motion . More precisely, the collision local time (in the sense of Barlow et al. ⁽¹⁾) of an underlying Brownian motion path W with the catalytic mass process goerns the branching (in the sense of Dynkin's additive functional approach). In the one-dimensional case, a new type of limit behavior is encountered: The total mass process converges to a limit without loss of expectation mass (persistence) and with a nonzero limiting variance, whereas starting with a Lebesgue measure , stochastic convergence to occurs.     

具广义功能反应函数非自治捕食系统的持久性和概周期问题

针对既有捕食关系,有竞争关系的三种群混合非自治捕食系统,将经典的Holling功能反应函数推广为广义功能反应函数,通过构造Liapunov函数,运用常微分方程定性理论知识,研究了系统的持续性和全局渐近稳定性,并进一步讨论了此系统的正概周期解的存在性和稳定性,得到了系统存在唯一、全局渐近稳定正概周期解的充分条件,对已有的结论进行了较大程度的推广.     

一类食饵具有投放率和捕食者具有捕获率的非自治捕食系统的全局分析

研究了一类具有Beddington-DeAngelis类功能反应以及捕食者具有捕获率和食饵具有投放率的非自治系统,用微分方程稳定性理论及构造Liapunov函数获得系统持续生存和全局稳定的充分条件.     

Influence of Soil Moisture and Vegetation on Climate (Ⅱ)——Numerical Experiments on Persistence of Short-term Climatic Anomalies

Numerical experiments on the influence of soil moisture and vegetation on the persistence of short-term climatic anomalies are performed with a vertical one-dimensional climate model in the atmosphere-soil-vegetation system.The experimental results indicate that, as shown by theoretical analysis in Part Ⅰ of this paper,soil hydrology is crucially important for maintenance of short-term climatic anomalies over land areas. Possible physical process concerned with impact of soil moisture and vegetation on the persistence is further discussed.