本文關鍵詞： 戰(zhàn)爭模型 不確定因素 It(?)微積分 馬爾可夫性　出處：《湖北工業(yè)大學》2017年碩士論文　論文類型：學位論文

【摘要】：本文分析了戰(zhàn)爭中雙方戰(zhàn)斗人數(shù)的不確定性因素,論述了戰(zhàn)爭中戰(zhàn)斗人數(shù)變化是一個隨機過程,通過假設戰(zhàn)爭過程具有馬爾可夫性質,從而在經典戰(zhàn)爭模型的基礎上建立了三種戰(zhàn)爭的隨機微分方程模型.正規(guī)戰(zhàn)爭的隨機微分方程模型該模型為線性的,因此本文使用常數(shù)變易法依據(jù)Ito積分規(guī)則,求解了這個模型的Ito解,得到了雙方勝負的判別依據(jù).游擊戰(zhàn)爭的隨機微分方程模型由于此模型為非線性的,難以得到解析表達式,故本文采用定性的分析方法研究了游擊戰(zhàn)爭隨機模型,并得到雙方勝負的部分判斷條件.混合戰(zhàn)爭的隨機微分方程模型在混合戰(zhàn)爭的隨機微分方程模型的研究中,本文借用了隨機微分方程的比較定理方法分析得出了此模型中雙發(fā)勝負的條件.最后使用matlab編程對建立的模型進行了數(shù)值模擬計算,對得到的雙方勝負的判別結論加以驗證.并以硫磺島戰(zhàn)役為實際例子,比較了確定性的微分方程方程和不確定性的隨機方程建立的模型在描述正規(guī)戰(zhàn)爭的差異,數(shù)值模擬表明概率與微分方程建立的模型描述戰(zhàn)爭過程更為精確.
[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.
【學位授予單位】：湖北工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.63

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本文編號：1520619