捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.     

The asymptotic analysis of an insect dispersal model on a growing domain

This paper is concerned about a reaction-diffusion equation on n-dimensional isotropically growing domain, which describes the insect dispersal. The model for growing domains is first derived, and the comparison principle is then presented. The asymptotic behavior of the solution to the reaction-diffusion problem is given by constructing upper and lower solutions. Our results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution. Numerical simulations are also performed to illustrate the analytical results.     

Effects of population dispersal and impulsive control tactics on pest management

In this paper, we firstly consider a Lotka–Volterra predator–prey model with impulsive constant releasing for natural enemies and a proportion of killing or catching pests at fixed moments, and we have proved that there exists a pest-eradication periodic solution which is globally asymptotically stable. Further, we extend the model for the population to move in a two-patch environment. The effects of population dispersal and impulsive control tactics are investigated, i.e. we chiefly address the question of whether population dispersal is beneficial or detrimental for pest persistence. To do this, some special cases are theoretically investigated and numerical investigations are done for general case. The results indicate that for some ranges of dispersal rates, population dispersal is beneficial to pest control, but for other ranges, it is harmful. These clarify that we can get some new effective pest control strategies by controlling the dispersal rates of pests and natural enemies.     

A REACTION–DIFFUSION EQUATION MODELING THE INVASION OF THE ARGENTINE ANT POPULATION,LINEPITHEMA HUMILE,AT JASPER RIDGE BIOLOGICAL PRESERVE

Abstract A continuous reaction–diffusion model is developed for the invasive Argentine ant population within a preserve in northern California. The model is a second‐order partial differential equation incorporating a logistic growth term. The dispersal distance traveled during the reproductive process of budding is used to estimate the diffusion coefficient. The model has two homogeneous steady states, one occurring at the propagation front where the Argentine ant population does not yet exist and one occurring where the population has reached carrying capacity. The traveling wave solutions of the model depict the population density for a given time and location. Using current research, parameter values for the model are estimated and a traveling wave solution for the average parameter values is numerically demonstrated.     

Direct spatial optimization in natural resource management: Four linear programming examples

This paper discusses methods for directly incorporating spatial relationships in natural resource optimization models. The approaches are contrasted with the conventional emphasis on adjacency restrictions. Four formulations are presented that address a variety of problems using linear (continuous-variable) programming, which allows reliable solvability of even very large models. The problems addressed include: habitat placement for the black-footed ferret (an aggressive disperser), habitat placement for the black-tailed prairie dog (a gregarious, recalcitrant disperser), placement of control efforts directed at restricting the spread of an exotic pest, and the semi-permanent placement of habitat for the northern spotted owl (a static problem).     

基于分形维数的液体爆炸分散中界面破碎形态研究

通过对爆炸抛撒图象的处理,得到液体界面的曲线.采用盒维数的计算方式,计算界面曲线的分形维数.通过对各时刻液体界面分形维数的变化研究,分析爆炸抛撒近场阶段的变化过程,同时观察到蘑菇状尖顶的出现与破碎,以及空化区域的形成和消失现象。     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

计算机辅助彩色立体图像生成中的误差分析与处理

柱透镜光栅的计算机辅助立体成像的基本原理是将二维序列图像进行切分和重组,使之以三维模型的形式展现,使合成的图像在柱透镜光栅下观察时具有"纵深感"。该项技术在广告、摄影、电影制作中具有广泛的应用。但是长期以来,在图像切分时并不能保证像素一定被整除,这意味着剩余像素的出现,合成的立体图像必然存在误差。如何处理剩余像素的问题一直是个难题,阻碍了该技术的推广。针对立体图像生成方法中的剩余像素问题,详尽地分析了误差的形成,并提出了强行取整算法和误差分散算法两种误差处理方法。实验表明,这两种算法能较好的处理剩余像素,增强了合成图像的立体效果,这将有助于立体成像技术的进一步推广。     

On the stability of a population model with nonlocal dispersal

This paper is concerned with a nonlocal dispersal population model with spatial competition and aggregation. We establish the existence and uniqueness of positive solutions by the method of coupled upper-lower solutions. We obtain the global stability of the stationary solutions.     

两斑块间具有非对称双向脉冲扩散的周期单种群模型

研究了两斑块间具有脉冲扩散的周期单种群模型。利用脉冲微分方程的比较原理和一些分析方法,得到了系统持久性的充分条件,然后利用Brouwer不动点理论和构造Lyapunov函数的方法,得到了系统正周期解全局渐近稳定的充分条件。