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生物数学 1997年第1期1卷 1-7页

作者：陈兰荪俞军南京理工大学生物数学研究中心

本文总结了近年来我们对斑块环境的非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ模型所做的一些研究工作，得到了这类系统的持续生存性、周期解的存在唯一性和全局渐近稳定性的条件，并讨论了扩散的影响。

关键词：数学生态学种群 lotka-volterra 扩散系统

具有毒素影响的非简化二维lotka－volterra模型

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大连轻工业学院学报 1995年第1期14卷 54-59页

作者：闫慧臻大连轻工业学院数学教研室

本文研究了具有毒素影响的非简化二维Ｖｏｌｔｅｒｒａ模型，给出了两种群持续生存与绝灭的一些充分条件，从而为实际应用提供了一定的理论依据。

关键词：种群持续生存绝灭 lotka-volterra 模型毒素

共生理论视域下区域智库联盟演进路径与发展机制研究

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智库理论与实践 2024年第4期9卷 66-78页

作者：朱婧祎李北伟李瑞李麟白吉林大学商学与管理学院长春130012 宿迁学院经济管理学院宿迁223800

[目的/意义]区域智库联盟是中国特色新型智库建设的重要载体。本文结合共生理论探讨区域智库联盟演进路径和发展机制,以期拓展智库联盟相关研究,为区域智库联盟稳定发展提供有益参考。[方法/过程]首先,在明晰区域智库联盟共生系统要素... 详细信息

[目的/意义]区域智库联盟是中国特色新型智库建设的重要载体。本文结合共生理论探讨区域智库联盟演进路径和发展机制,以期拓展智库联盟相关研究,为区域智库联盟稳定发展提供有益参考。[方法/过程]首先,在明晰区域智库联盟共生系统要素构成的基础上,从共生组织模式和共生行为模式两个方向分析区域智库联盟演进路径;然后,构建基于lotka-volterra方程的区域智库联盟共生演化模型,并通过模型的稳定性条件分析和模拟仿真讨论不同共生行为模式下联盟成员相互作用的演化规律以及平衡状态;最后,提出区域智库联盟共生发展机制。[结果/结论]基于质参量兼容原理、共生能量生成原理、共生系统进化原理和共生系统相变原理,区域智库联盟共生发展机制包括环境引导机制、界面增容机制、能量协调机制和新陈代谢机制。

关键词：区域智库联盟共生理论 lotka-volterra 模型仿真

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Dirac Concentrations in a Chemostat Model of Adaptive Evolution(In honor of the immense scientific influence of Ham Brezis)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 513-538页

作者： Alexander LORZ Benoit PERTHAME Cécile TAING Sorbonne Universits UPMC Univ Paris 06InriaLaboratoire Jacques-Louis Lions UM R CNRS 7598F75005 ParisFrance

This paper deals with a non-local parabolic equation of lotka-volterra type that describes the evolution of phenotypically structured populations. Nonlinearities appear in these systems to model interactions and competition phenomena leading to selection. In this paper, the equation on the structured population is coupled with a differential equation on the nutrient concentration that changes as the total population *** methods aimed at showing the convergence of the solutions to a moving Dirac mass are reviewed. Using either weak or strong regularity assumptions, the authors study the concentration of the solution. To this end, BV estimates in time on appropriate quantities are stated, and a constrained Hamilton-Jacobi equation to identify where the solutions concentrates as Dirac masses is derived.

关键词： Adaptive evolution, Asymptotic behaviour, Chemostat, Dirac concentrations,Hamilton-Jacobi equations, lotka-volterra equations, Viscosity solutions

GLOBAL ATTRACTIVITY IN A N-SPECIES COMPETITION DIFFERENCE SYSTEM

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生物数学学报 1995年第3期10卷 1-8页

作者： Yuan Cunde Cui Xiaoying Liu Pingzhou(Shanxi Normal University,Linfen,Shanxi 041004)

A population of interacting species is considered which is governed by a system of nonlinear difference *** the case of the interacting species with competition,a sufficient condition for global attractivity of an equ... 详细信息

关键词： lotka-volterra difference equations competition global attractivity.

Understanding the Competitive and Cooperative Interactions between Probiotics and Autochthonous Intestinal Bacteria

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Journal of Biosciences and Medicines 2017年第4期5卷 63-80页

作者： Tyler Brown Majid Bani-Yaghoub Jose F. García-Mazcorro Department of Biological Engineering University of Missouri-Columbia Columbia Missouri USA Department of Mathematics and Statistics University of Missouri-Kansas City Kansas City Missouri USA Facultad de Medicina Veterinaria y Zootecnia Universidad Autónoma de Nuevo León General Escobedo Nuevo León México

The present study combines the theory and the experimental data to predict the changes on intestinal bacterial populations during ingestion of beneficial probiotic bacteria. Our proposed model is a modified version of the lotka-volterra model, which takes the probiotic administration into account. Using the linear stability analysis of the model, the conditions for coexistence of the probiotics with other bacteria are established. Using the model fitted to the data of C. coccoides species and Bifidobacterium species, the effects of oral probiotics on autochthonous bacterial cultures is investigated. The estimated parameter values suggest that C. coccoides and Bifidobacterium facilitate each other during the probiotics administration, whereas they compete in the absence of the probiotics administration. This may suggest the beneficial effect of probiotic administration as it promotes the growth of C. coccoides species. The results also confirm prior studies showing that once probiotic supplementation is discontinued, the probiotic population and the promoting effect within the digestive tract will diminish.

关键词： Bifidobacterium C. coccoides lotka-volterra Model Probiotics Stability Analysis

Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation

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Journal of Applied Mathematics and Physics 2015年第5期3卷 496-508页

作者： Xiaorong Hu Yanbin Tang Department of Mathematics National University of Defense Technology Changsha China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China

This paper considers the asymptotic dynamics of steady states to the lotka-volterra competition diffusion systems with random perturbations by two-parameter white noise on the whole real line. By the fundamental solution of heat equation, we get the asymptotic fluctuating behaviors near the stable states respectively. That is, near the steady state (u,v)=(0,1), the mean value Eu(x,t) is shifted above the equilibrium u=0 and Ev(x,t) is shifted below the equilibrium v=1. However, near the steady state (u,v)=(1,0), the mean value Eu(x,t) is shifted below the equilibrium u =1 and Eu(x,t)=0.

关键词： lotka-volterra Competition Diffusion System Random Perturbation Two-Parameter White Noise

Hopf Bifurcations in a Predator-Prey System of Population Allelopathy with Discrete Delay

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Applied Mathematics 2012年第6期3卷 652-661页

作者： Xinhui Wang Haihong Liu Department of Mathematics Yunnan Normal University Kunming China

A delayed lotka-volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, some numerical simulations are carried out for illustrating the theoretical results.

关键词： lotka-volterra Predator-Prey System Discrete Delay Allelopathy Stability Hopf Bifurcation Periodic Solution

电子商务模式模仿者与创新者竞争动态研究——当当网和亚马逊中国竞争演变分析

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科学学与科学技术管理 2013年第6期34卷 44-51页

作者：王砚羽谢伟清华大学经济与管理学院北京100084

利用竞争扩散模型lotka-volterra分析了我国书籍网购市场中当当网和亚马逊中国这两个主要竞争者的市场竞争动态。从模型的分析效果来看,lotka-volterra模型在分析竞争性市场中更具有适用性,并且比Logistic模型具有更好的拟合度;从分析... 详细信息

利用竞争扩散模型lotka-volterra分析了我国书籍网购市场中当当网和亚马逊中国这两个主要竞争者的市场竞争动态。从模型的分析效果来看,lotka-volterra模型在分析竞争性市场中更具有适用性,并且比Logistic模型具有更好的拟合度;从分析结果来看,当当网在独占性市场的发展动力大于亚马逊中国,同时当当网在模仿创新过程中获得了一定的收益;但当当网和亚马逊中国的竞争关系为被捕食者—捕食者关系,并且当当网的进攻优势只是亚马逊中国反击能力的一半;当当网和亚马逊中国在近几年中将不会出现平衡点,两者差距将逐渐增大。

关键词： lotka-volterra 当当网亚马逊中国商业模式创新

高技术服务创新网络生态位重叠企业竞合关系建模与仿真

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科技进步与对策 2014年第13期31卷 59-63页

作者：孙耀吾韩冰黄万艮湖南大学工商管理学院湖南长沙410082

在高技术服务创新网络中,参与主体生态位重叠与竞合关系复杂。应用生态位理论中lotka-volterra原理,构建企业生态位演化模型群,并进行系统仿真,揭示不同类型高技术服务创新网络参与主体的动态竞合关系。研究结果表明,生态位重叠的创新... 详细信息

在高技术服务创新网络中,参与主体生态位重叠与竞合关系复杂。应用生态位理论中lotka-volterra原理,构建企业生态位演化模型群,并进行系统仿真,揭示不同类型高技术服务创新网络参与主体的动态竞合关系。研究结果表明,生态位重叠的创新主体间只有采取合作共生模式,才会产生企业生态位协同进化;片面追求自身发展的单向思维模式,反而可能导致企业生态位被逐渐侵蚀。该研究结论对于探索科学治理创新网络、促进企业协同发展具有重要启示。

关键词：高技术服务创新网络生态位重叠 lotka-volterra 模型竞合关系