一类Lotka-Volterra模型的解析定量研究  

Analytically Quantitative Studies on a Lotka-Volterra Model

作　　者：沈建和[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《漳州师范学院学报（自然科学版）》2010年第4期13-18,共6页Journal of ZhangZhou Teachers College（Natural Science)

基　　金：福建省教育厅A类项目(JA10065)

摘　　要：利用经典的Lindstedt-Poincare(L-P)法及一种改进的L-P法,研究一类Lotka-Volterra模型的定量特征,获得了该模型周期解的解析近似表达式及周期解周期的解析近似式.研究结果表明:两种L-P法的结果在确定的近似阶数下是完全相同的.与数值积分结果比较表明:两种L-P法所得的解析结果都具有较高的精度,特别是当初始值不太大时.Using the classical L-P method and a modified L-P method,quantitative aspects of a Lotka-Volterra model is studied analytically.The analytically approximate expressions of the periodic solutions and their period are obtained.It is showed that the analytical results of the classical and modified L-P methods are identical under certain order of approximation.Comparisons with the numerical integration results show that the analytical results of two L-P methods are quite accurate,especially for the small initial values.

关 键 词：LOTKA-VOLTERRA模型 L-P法 周期解 定量研究 

分 类 号：O175.1[理学—数学]