一类具有离散时滞的非自治扩散的两种群模型的一致持续生存

持续生存概念是种群生态系统稳定性的一个重要描述,而研究竞争种群共存的问题是种群生态学的一个重要问题.进一步考虑具有离散时滞的非自治的两种群竞争扩散摸型,使模型更符合其生态意义,通过微分不等式获得了其一致持续生存的充分条件.     

复杂生态系统的模糊数学模型

生态系统是一个复杂的大系统，很多重要的生态学理论问题都是以生态位(niche)和生物群落概念为基础的。本文将生态位和群落抽象出来，看作是一个耗散结构。建立生态系统中基本概念的量化算子，利用系统模糊分析理论给出具有明确生物意义的生态位和群落的Fuzzy数学模型。并以此讨论生态系统中其他相关概念的数学模型、群落的水平和垂直格局及物种间在资源、斑块、时间三维模糊集上的互惠，共处和竞争关系。初步构建起复杂生态大系统的数学理论框架。     

非线性生态系统的复杂动力学行为研究(Ⅰ)

本文丛拟系统讨论非线性生态系统的复杂动力学行为及其内在机制.本文简要论述了生态学研究日益重要的意义,述评了生态理论落后于社会实践的状况和原因,指出了现代生态学研究所应遵从的程序;比较详细地论述了生态系统的四个基本特征:层次性、开放性、非线性与远离平衡;最后系统地论述了非线性生态系统的平衡与非平衡、稳定与不稳定以及动态行为的外在随机性和动力随机性,指出在非线性生态系统的确定性行为和随机行为之间存在由此及彼的桥梁,由此将导致生态预测新模式.     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

数学建模——科学培养数学思维的关键

数学建模是训练数学思维的重要手段,是科学培养数学思维的关键.从数学建模过程对于科学地训练数学思维的作用出发,对数学建模和数学思维的能动关系进行了理论研究,分别从理论基础和实际应用两个方面说明数学建模教学等相关活动的开展对于科学地培养数学思维的重要作用.     

生物学中的数学建模

生物学与其它学科的交叉是近年来学术界讨论的一个重要话题 .系统科学这一类横断科学从其产生之初就具有其鲜明的一般性和普适性 ,尤其适合对生命这一开放的、有序的、复杂的系统进行研究和探讨 .近年来 ,这方面的发展非常迅速 ,生物学研究的新思路、新方法层出不穷 ,这无疑为广大研究人员带来崭新的研究工具和更优化的解决方案 .本文从生物建模的角度对这方面最新的研究进展进行总结、归纳 ,以求集思广益、触类旁通 .     

具有连续时滞的非自治扩散Lotka-volterra模型的渐近性

持续生存概念是种群生态系统稳定性的一个重要描述,而研究竞争种群共存的问题是种群生态学的一个重要问题,考虑非自治的两种群L otka-vo lterra周期系数的时滞扩散摸型,通过构造李亚普诺夫泛函,微分不等式等获得了其一致持续生存及正周期解存在与全局渐近稳定的充分条件.     

函数极值原理在动物行为建模中的应用

1　前　　言数学模型在生态和进化生物学的发展过程中起到了一个极为重要的作用.本世纪二十年代出现的Lotka和Volterra的捕食者——猎物模型帮助建立起了动物种群动态的生态学研究.大约在同一时期由Haldane,Fisher和Wright发展起来的种群遗传模型证实和演示了Mendel遗传原理的有效性.自那以后,数学模型一直指导着定量和直观地描述了多种生物现象,如生活史策略,性比进化,觅食行为优化,等等。令人惊奇的是,数学的精确性在描述特别复杂的生态和进化相互关系中起到了不可替代的重要作用(Othmeretal.,1997).在过去二十年间,动物行为生态由一个…     

一类非线性等级结构种群控制模型解的适定性

分析一类具有个体年龄等级差异的非线性种群系统模型解的适定性问题.运用特征线法、积分不等式和不动点原理证明了系统非负解的存在唯一性和有界性,以及解对控制变量的一致连续性.拓展了常见的年龄结构系统基本理论.为研究种群的长期演化和调控问题奠定基础.     

生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析

为研究生境修复对生态系统产生的影响,文章建立了一类在生境破坏情况下,具有Monod-Haldane功能反应,脉冲比例收获和脉冲常数投放的四种群食饵-捕食者模型.利用脉冲比较定理,Floquent理论及微小扰动法研究了系统的动力学性质,并给出系统中两食饵灭绝和种群持续生存的充分条件.最后,通过数值模拟验证了所得结论.结果显示系统存在一定脆弱性和复杂性,随着生境修复比率和捕食者投放比率的变化,系统将出现拟周期,混沌等复杂的动力学现象.环境修复作用对系统影响的复杂性,也体现了生境修复的重要性.     

Analysis of a class of Kolmogorov systems

A two-dimensional Kolmogorov system depending on two independent parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the origin. The behavior of the system is described by bifurcation diagrams. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.     

Predator–prey interaction system with mutually interfering predator: role of feedback control

In this study, we investigate the global dynamics of non-autonomous and autonomous systems based on the Leslie–Gower type model using the Beddington–DeAngelis functional response (BDFR) with time-independent and time-dependent model parameters. Unpredictable disturbances are introduced in the forms of feedback control variables. BDFR explains the feeding rate of the predator as functions of both the predator and prey densities. The global stability of the unique positive equilibrium solution of the autonomous model is determined by defining an appropriate Lyapunov function. The condition obtained for the global stability of the interior equilibrium ensures that the global stability is free from control variables, which is also a significant issue in the ecological balance control procedure. The autonomous system exhibits complex dynamics via bifurcation scenarios, such as period doubling bifurcation. We prove the existence of a globally stable almost periodic solution of the associated non-autonomous model. The different coefficients of the system are taken as almost periodic functions by generalizing periodic assumptions. The permanence of the non-autonomous system is established by defining upper and lower averages of a function. Our results also explain how the important hypothesis in ecology known as the “intermediate disturbance hypothesis” applies in predator–prey interactions. We show that moderate feedback intensity can make both the ordinary differential equation system and partial differential equation system more robust. The results obtained provide new insights into the protection of populations, where moderate feedback intensity can promote the coexistence of species and adjusting the intensity of the feedback in appropriate regions can control the population biomass while maintaining the stability of the system. Finally, the results obtained from extensive numerical simulations support the analytical results as well as the usefulness of the present study in terms of ecological balance and bio-control problems in agro-ecosystems.     

Analysis of a class of dynamic programming models for multi-stage uncertain systems

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. This paper deals with the optimal control problem for a multi-stage dynamic system in an indeterminate environment. Firstly, we formulate a practical uncertain control model based on the critical value criterion and present recursion equations for this model based on Bellman’s Principle. A special linear model is shown to illustrate how the recursion equations operate to obtain the analytical solution. Furthermore, we demonstrate a hybrid intelligent algorithm to evaluate and approximate the optimal solutions of more general cases. Finally, a discrete version of the production-inventory problem is discussed and numerically analyzed to illuminate the effectiveness of the methodology.     

A simple Gause‐type predator–prey model considering social predation

The consumer–resource relationships are among the most fundamental of all ecological relationships and have been the focus of ecology since its beginnings. Usually are described by nonlinear differential equation systems, putting the emphasis in the effect of antipredator behavior (APB) by the prey; nevertheless, a minor quantity of articles has considered the social behavior of predators. In this work, two predator–prey models derived from the Volterra model are analyzed, in which the equation of predators is modified considering cooperation or collaboration among predators. It is well known that competition among predators produces a stabilizing effect on system describing the model, since there exists a wide set in the parameter space where the system has a unique equilibrium point in the phase plane, which is globally asymptotically stable. Meanwhile, the cooperation can originate more complex and unusual dynamics. As we will show, it is possible to prove that for certain subset of parameter values the predator population sizes tend to infinite when the prey population goes to extinct. This apparently contradicts the idea of a realistic model, when it is implicitly assumed that the predators are specialist, ie, the prey is its unique source of food. However, this could be a desirable effect when the prey constitutes a plague. To reinforce the analytical result, numerical simulations are presented.     

Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment

In this paper, we consider a two-dimensional model for two competitive phytoplankton species where one species is toxic phytoplankton and other is non-toxic species. The logistic growth of both the species follows the Hutchinson type growth law. First, we briefly discuss basic dynamical properties of non-delayed and delayed model system within deterministic environment. Next we formulate the stochastic delay differential equation model system to study the effect of environmental driving forces on the dynamical behavior. We calculate population fluctuation intensity (variance) for both species by Fourier transform method. Numerical simulations are carried out to substantiate the analytical findings. Significant results of our analytical findings and their interpretations from ecological point of view are provided in concluding section.     

MATHEMATICAL STUDY OF A PEST CONTROL MODEL INCORPORATING STERILE INSECT TECHNIQUE

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results.     

信息技术与大学数学课程整合的方式与理论探讨

信息技术与大学数学课程整合正成为当前我国信息技术教育乃至整个教育信息化进程中的一个热点问题,探讨其整合的方式及理论基础是非常必要的.本文首先结合大学数学案例探讨了整合的三种方式:动态的课堂演示型、单机的数学实验型和全交互的网络教学型,其次探讨了整合所依据的四种理论:传播理论、建构主义理论、教学设计理论和系统理论,最后提出了自己对信息技术与大学数学课程整合的一些思考.     

Bayesian spatial modeling of genetic population structure

Natural populations of living organisms often have complex histories consisting of phases of expansion and decline, and the migratory patterns within them may fluctuate over space and time. When parts of a population become relatively isolated, e.g., due to geographical barriers, stochastic forces reshape certain DNA characteristics of the individuals over generations such that they reflect the restricted migration and mating/reproduction patterns. Such populations are typically termed as genetically structured and they may be statistically represented in terms of several clusters between which DNA variations differ clearly from each other. When detailed knowledge of the ancestry of a natural population is lacking, the DNA characteristics of a sample of current generation individuals often provide a wealth of information in this respect. Several statistical approaches to model-based clustering of such data have been introduced, and in particular, the Bayesian approach to modeling the genetic structure of a population has attained a vivid interest among biologists. However, the possibility of utilizing spatial information from sampled individuals in the inference about genetic clusters has been incorporated into such analyses only very recently. While the standard Bayesian hierarchical modeling techniques through Markov chain Monte Carlo simulation provide flexible means for describing even subtle patterns in data, they may also result in computationally challenging procedures in practical data analysis. Here we develop a method for modeling the spatial genetic structure using a combination of analytical and stochastic methods. We achieve this by extending a novel theory of Bayesian predictive classification with the spatial information available, described here in terms of a colored Voronoi tessellation over the sample domain. Our results for real and simulated data sets illustrate well the benefits of incorporating spatial information to such an analysis.     

Mathematical analysis and numerical simulation of pattern formation under cross-diffusion

Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in the study of the spatial distribution of species in ecological systems. This paper is concerned with some mathematical and numerical aspects of a particular reaction–diffusion system with cross-diffusion, modeling the effect of allelopathy on two plankton species. Based on a stability analysis and a series of numerical simulations performed with a finite volume scheme, we show that the cross-diffusion coefficient plays a important role on the pattern selection.