兰彻斯特方程的渐近解分析

Asymptotic Analysis of Lanchester Equation

建立了带有延迟小参数的兰彻斯特方程,利用时滞摄动理论求出了相应方程的渐近解,从而定量地描述作战双方的兵力变化以及时滞因素对战争胜负的影响。最后用构造上下解方法证明了渐近解的一致有效性。

This paper built delay Lanchester equation, and by using delay singular perturbation theories and methods got asymptotic solution of equation. Then, it described quantitatively the forces change of both sides of the combat and the impact of delay factor on the outcome of war. Last, it analyzed the uniform validity of solution.