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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