Two-Dimensional Nonlinear Dynamic System Model of Interspecific Interaction and Numerical Simulation Research on It
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摘要: 系统探讨了种间制约作用的二维非线性动力系统的机理与过程,从生物力学角度扩展了Lotka-Volterra模型,建立了包含种间作用与反作用的二维非线性自治、非自治动力系统新模型,分析了该动力系统平衡点的稳定性、周期解的存在性与稳定性,并对其动力学过程进行了数值模拟试验研究.结果表明两生物种群间作用效率的大小、作用系数与反作用系数变化的同向与异向性和作用力时变等对动力系统稳定性都有一定影响,种间作用效率变大或变小,以及作用系数与反作用系数的异向变化都导致动力系统的不稳定,致使两种生物难以生存,而相互作用力时变则对系统的稳定起促进作用.Abstract: The mechanism and the course of two-dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically.By extending the Lotka-Volterra model from the viewpoint of biomechanics,it developed new models of two-dimensional nonlinear autonomous and nonautonomous dynamic systems,with its equilibrium point s stability and the existence and stability of its periodical solutions analyzed,and did numerical simulation experiments on its dynamics course.The results show that efficiency of interaction between two populations,time-varying effort,and change direction of action coefficient and reaction coefficient have important influences on the stability of dynamic system,that too large or too small interspecific interaction efficiency and contrary change direction of action coefficient and reaction coefficient may result in the nonstability of the system,and thus it is difficult for two populations to coexist,and that time-varying active force contributes to system stability.
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[1] 张大勇.理论生态学研究[M].北京:高等教育出版社,施普格林出版社,2000. [2] 陈兰荪,陈健.非线性生物动力系统[M].北京:科学出版社,1993. [3] 原存德,裴永珍.具有不同扩散率的两种群Ayala竞争模型的持续生存[J].应用数学和力学,1999,20(4):443-440. [4] 张银萍,孙继涛.三种群Lotka-Volterra非周期食饵-捕食系统的持久性[J].应用数学和力学,2000,21(8):792-796. [5] 郭瑞海,袁晓凤.一类微生物种群生态数学模型的Hopf分支[J].应用数学和力学,2000,21(7):693-700. [6] 李骊.强非线性振动系统的定性理论与定量方法[M].北京:科学出版社,1997. [7] 凌复华.非线性动力系统的数值研究[M].上海:上海交通大学出版社,1989. [8] Myerscough M R,Darwen M J,Hogarth W L.Stability,persistence and structural stability in a classical predator-prey model[J].Ecological Modelling,1996,89:31-42. [9] 林建忠,林江,朱丽兵.气固两相圆射流场涡结构影响因粒扩散的研究[J].应用数学和力学,1999,20(5):470-476. [10] 王银邦.非轴对称载荷作用的外部圆形裂纹问题[J].应用数学和力学,2001,22(1):9-15. [11] 黄先开,董勤喜.具有时滞的高维周期系统的周期解[J].应用数学和力学,1999,20(8):847-850. -
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