广义Lotke-Volterra非线性生态模型的渐近解(英文)  

Asymptotic Solution for GeneralizedLotke-Volterra Nonlinear Ecological

作　　者：陈丽华[1] 姚静荪[2] 莫嘉琪[2,3] 

机构地区：[1]福建师范大学福清分校数学与计算机科学系,福建福清350300 [2]安徽师范大学数学系,安徽芜湖241000 [3]湖州师范学院理学院,浙江湖州313000

出　　处：《南开大学学报（自然科学版）》2011年第6期62-67,共6页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the National Natural Science Foundation of China(40876010);the "Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues" of the Chinese Academy of Sciences(XDA01020304);the LASG State Key Laboratory Special Fund,China,the Natural Science Foundation of Zhejiang Province,China(Y6110502);the Natural Science Foundation of Jiansu Province(BK2011042);the Natural Science Foundation from the Education Bureau of Anhui Province,China(KJ2011A135);the Foundation of the Education Department of Fujian Province(JA10288)

摘　　要：研究了非线性广义Lotke-Volterra生态模型,首先利用简单而有效的摄动方法,研究了一个种群生态模型,它是一个微分方程系统.然后利用摄动方法得到了原问题解的渐近展开式,并得到了它是原模型解是一个好的近似的结论.这是一个解析展开式并且能保持其解析运算.最后,给出了一个对应的例子,它说明了得到的解具有很好的精度,从而由模型的渐近展开式能进一步从解析的观点去预测和探讨有关生态的规律.The nonlinear generalized Lotke-Volterra ecological model is studied. A perturbation method, being simple and valid, is applied to study the species group ecological model. First, a ecological is studied, which is a system of differential equation. Then, using the perturbation method the asymptotic expansions of solution for the original problem are obtained. The conclusion is that a good approximation for the original mod- el comes to a solution, which is an analytic expression, and can keep on analytic operation. Lastly, a corre- sponding example is given, which show that the obtained solution possesses a very good accuracy. Thereby, the expansions for solution of model, from the analytical point of view, the disciplinarian of ecological can forecast and discussed ulteriorly.

关 键 词：非线性 Lotke—Volterra生态模型 奇摄动 

分 类 号：O175.14[理学—数学]