【摘要】：近年來,計算機病毒的防治受到專家、學者以及社會各界人士的廣泛關注,并成為互聯(lián)網(wǎng)信息安全領域最具挑戰(zhàn)性和最難攻克的難題之一.深入了解計算機病毒的特點和傳播規(guī)律,進而建立病毒傳播模型可以有效預測和控制計算機病毒的傳播,并對建設安全和諧的網(wǎng)絡環(huán)境起到積極推動作用.主要研究成果如下:①基于用戶是否會預先安裝殺毒軟件與其對病毒的危害意識強弱有關,從而對一類分段SIRS病毒傳播模型進行改進.主要研究了新模型的兩類平衡點(無毒平衡點和病毒平衡點)的穩(wěn)定性.首先推導出系統(tǒng)平衡點的存在性條件.其次,通過求系統(tǒng)在平衡點處的Jacobi矩陣的特征值來判斷平衡點的局部穩(wěn)定性.然后,構(gòu)造Lyapunov函數(shù)進一步證明平衡點的全局穩(wěn)定性.最后,數(shù)值仿真驗證系統(tǒng)的平衡點是全局穩(wěn)定的.②基于殺毒軟件的殺毒能力與殺毒軟件的成本有關,提出了一個分段SIQRS計算機病毒傳播模型.主要研究了該模型的兩類平衡點的穩(wěn)定性.首先推導出系統(tǒng)的基本再生數(shù)和平衡點的存在性條件.其次,借助Routh-Hurwitz判別法和中心流形定理證明平衡點的局部穩(wěn)定性.接著,構(gòu)造Lyapunov函數(shù)并根據(jù)LaSalle不變原理證明平衡點的全局穩(wěn)定性.然后,數(shù)值仿真驗證結(jié)論的正確性.最后,討論了系統(tǒng)的參數(shù)對基本再生數(shù)的影響,從而提出了三種有效的防御措施.
[Abstract]:In recent years, the prevention and treatment of computer virus has been widely concerned by experts, scholars and people from all walks of life, and has become one of the most challenging and difficult problems in the field of Internet information security. By deeply understanding the characteristics and spreading rules of computer virus, establishing a virus transmission model can effectively predict and control the spread of computer virus, and play an active role in promoting the construction of a safe and harmonious network environment. The main research results are as follows: 1 based on whether the user will install antivirus software in advance, it is related to the harm consciousness of the virus, so a class of segmented SIRS virus transmission model is improved. The stability of two kinds of equilibrium points (non-toxic equilibrium point and virus equilibrium point) of the new model is studied. First, the existence condition of equilibrium point of the system is derived. Secondly, the local stability of the equilibrium point is determined by finding the eigenvalue of the Jacobi matrix at the equilibrium point. Then, the Lyapunov function is constructed to prove the global stability of the equilibrium point. Finally, numerical simulation shows that the balance point of the system is globally stable. 2 based on the antivirus ability of the antivirus software and the cost of the antivirus software, a segmented SIQRS computer virus transmission model is proposed. The stability of two kinds of equilibrium points of the model is studied. First, the basic reproducing number and the existence condition of equilibrium point of the system are derived. Secondly, the local stability of the equilibrium point is proved by using the Routh-Hurwitz criterion and the center manifold theorem. Then, the Lyapunov function is constructed and the global stability of the equilibrium point is proved according to the LaSalle invariant principle. Then, the numerical simulation verifies the correctness of the conclusion. Finally, the influence of system parameters on the basic reproduction number is discussed, and three effective defense measures are proposed.
【學位授予單位】：廣西大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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