空间曲线在奇异点处的性态

本文讨论了空间曲线ｘ＝ｘ（ｔ），ｙ＝ｙ（ｔ），ｚ＝ｚ（ｔ）上奇异点的性态，结果表明：若［ｘ（ｋ）（ｔ０）］２＋［ｙ（ｋ）（ｔ０）］２＋［ｚ（ｋ）（ｔ０）］２＝０，ｋ＝１，２，…，ｎ－１，而［ｘ（ｎ）（ｔ０）］２＋［ｙ（ｎ）（ｔ０）］２＋［ｚ（ｎ）（ｔ０）］２≠０，则当ｎ为奇数时，曲线在点Ｍ０（ｘ０，ｙ０，ｚ０）是光滑的；当ｎ为偶数时，曲线在点Ｍ０（ｘ０，ｙ０，ｚ０）是不光滑的     

种内竞争时滞对植被周期振荡模式的影响研究

考虑到干旱、半干旱地区的幼年植被与成年植被之间存在竞争水资源的现象,该文构建一个具有种内竞争时滞的植被-土壤水动力学模型。分析出系统存在植被灭绝平衡点和植被生存平衡点,并给出了平衡点局部稳定的条件,分别给出非空间系统和空间系统产生Hopf分支周期解的条件。通过数值模拟展示出两种系统对应的植被随时间演化做周期振荡模式,并通过参数敏感性分析发现降雨量和植被的增长率对这种模式的产生和模式的振幅、周期有显著影响,但蒸发量的影响效果最不显著,表明降雨量和植被本身的特征对干旱、半干旱地区植被的演化发展产生了深刻的影响。同时发现空间扩散的引入会抑制这种模式的发生,但对振幅和周期没有任何影响。所获得的结果解释了自然界中广泛观察到的植被周期振荡现象,为植被系统的可持续发展提供了理论支撑。     

A cellular automata model of epidemics of a heterogeneous susceptibility

In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible--infected--removed (SIR) epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell (or the degree of the scale-free networks) plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.     

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.     

一类SEIRS型流行病的细胞自动机模型

本文通过分析SEIRS类流行病，建立了该类疾病的二维概率细胞自动机模型。在二维中，每个细胞的状态代表易感者，潜伏者，患者，恢复者（或免疫者）和死亡者五个部分个体之一。我们研究了两种情况下，即对潜伏者和患者隔离与不隔离将对疾病转播的影响。经研究我们发现，如果不隔离疾病将持续流行，而及时的隔离则将会减缓疾病的流行。本模型给出了对具体疾病利用细胞自动进行仿真的算法。我们发现当恢复者的失去免疫力大于时，疾病潜伏者和患者的密度序列将在正平衡点附近振荡。最后，我们用计算机对模型进行了仿真。     

互惠系统的最优脉冲捕获

对两种群互惠系统的脉冲捕获问题进行了全面的研究.确定了在被捕获种群达到一定数量时,再进行脉冲捕获的最优捕获策略.这样既维持了种群的生态平衡,又使我们在捕获过程中的获利最大.     

环境污染中三维Volterra系统持续生存与绝灭的阈值

本文对环境容量很大且被污染的三种群系统进行了研究，得到了三维Volterra捕食-被捕食系统持续生存与绝灭的阈值．