一类带时滞的非线性兰彻斯特战斗模型的分析

基于非线性兰彻斯特方程的一般形式和现代战争的特点,考虑到时间因素在现代战争中的巨大作用,建立并讨论了一类带时滞的非线性兰彻斯特战斗模型。通过定性分析,得到了模型的平衡点及其稳定性,证明了原模型解的存在唯一性,并给出了解的存在区域。战例分析结果表明该模型能用来描述现代战争。因此,该模型对研究现代战争的战斗进程、武器发展规划、现代军事练兵等都具有一定的参考价值。

Analysis of a Class of Nonlinear Lanchester Combat Model with Time Delay

Based on the general form of the nonlinear Lanchester equation and the characteristics of modern warfare,taking the time factor into account,a class of nonlinear Lanchester combat model with time delay is established and investigated. Through the qualitative analysis,the model’s equilibrium and its stability are obtained. Moreover,the existence and uniqueness of the original model’s solutions is proved,and the existent region is given. The analysis results of an example battle show that the model can describe the modern warfare effectively. Consequently,the proposed model may provide a theoretical reference for analyzing the combat process of modern warfare,weapon development plan and the modern military training.