战争的随机微分方程建模与研究

发布时间：2018-02-21 01:34

本文关键词： 战争模型不确定因素 It(?)微积分马尔可夫性　出处：《湖北工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文分析了战争中双方战斗人数的不确定性因素,论述了战争中战斗人数变化是一个随机过程,通过假设战争过程具有马尔可夫性质,从而在经典战争模型的基础上建立了三种战争的随机微分方程模型.正规战争的随机微分方程模型该模型为线性的,因此本文使用常数变易法依据Ito积分规则,求解了这个模型的Ito解,得到了双方胜负的判别依据.游击战争的随机微分方程模型由于此模型为非线性的,难以得到解析表达式,故本文采用定性的分析方法研究了游击战争随机模型,并得到双方胜负的部分判断条件.混合战争的随机微分方程模型在混合战争的随机微分方程模型的研究中,本文借用了随机微分方程的比较定理方法分析得出了此模型中双发胜负的条件.最后使用matlab编程对建立的模型进行了数值模拟计算,对得到的双方胜负的判别结论加以验证.并以硫磺岛战役为实际例子,比较了确定性的微分方程方程和不确定性的随机方程建立的模型在描述正规战争的差异,数值模拟表明概率与微分方程建立的模型描述战争过程更为精确.
[Abstract]:This paper analyzes the uncertain factors of the number of combatants on both sides of the war, and discusses that the variation of the number of combatants in the war is a stochastic process. Based on the classical war model, the stochastic differential equation model of three kinds of wars is established. The stochastic differential equation model of normal war is linear. Therefore, the constant variable method is used in this paper according to the Ito integral rule. In this paper, the Ito solution of this model is solved, and the discriminant basis of both sides is obtained. Because the stochastic differential equation model of guerrilla warfare is nonlinear, it is difficult to obtain an analytical expression. In this paper, a qualitative analysis method is used to study the stochastic model of guerrilla warfare, and some judging conditions of victory and defeat are obtained. The stochastic differential equation model of mixed warfare is studied in the stochastic differential equation model of hybrid war. In this paper, by using the method of comparison theorem of stochastic differential equations, the conditions of double winning and losing in this model are obtained. Finally, the numerical simulation of the established model is carried out by using matlab programming. This paper verifies the conclusion of the two sides' victory and defeat, and takes the Battle of Iwo Jima as a practical example to compare the difference between the deterministic differential equation equation and the uncertain stochastic equation in describing the difference of the normal warfare. Numerical simulation shows that the model established by probability and differential equation is more accurate in describing the process of war.
【学位授予单位】：湖北工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63

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