一类非线性兰彻斯特方程的相轨线分析  

Phase trajectory analysis of a class of nonlinear Lanchester equation

作　　者：谢英超 程燕[1] 李文涛[1] 

机构地区：[1]陆军军官学院基础部,安徽合肥230031

出　　处：《合肥工业大学学报（自然科学版）》2015年第10期1437-1440,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11202106);安徽省自然科学基金资助项目(1408085MA06)

摘　　要：文章将基于非线性兰彻斯特方程的信息化战争模型转化为等价形式的数学模型,在一定区域内,讨论了该数学模型的奇点及其类型,并得到了模型的解的存在唯一性、相轨线的唯一性及其满足的方程。在相轨线方程及其唯一性的基础上,得到了预测战斗结局的判定定理,并进行了算例分析。结果表明,相轨线分析是研究该类兰彻斯特方程的行之有效的方法,可用来分析作战进程和预测战斗结局。In this paper, the information warfare models based on nonlinear Lanchester equations are transformed into an equivalent mathematical model, and the odd point and its style of the proposed mathematical model are discussed in the given area. Further, the existence and uniqueness of solution for the model are obtained, as well as the uniqueness of its phase trajectory and the equation that the phase trajectory satisfies. On the basis of the phase trajectory equation and its uniqueness, the judg- ment theorem for predicting battle ending is obtained and proved. Finally, the example analysis is done and the results show that the phase trajectory analysis is an effective method to study such Lan- chester equation. Consequently, the phase trajectory can be used to analyze operational process and p^edjct battle ending.

关 键 词：兰彻斯特方程 信息化战争 非线性 相轨线 预测战斗结局 

分 类 号：E911[军事] O175.14[理学—数学]