两类分段计算机病毒传播模型的稳定性分析
发布时间：2018-10-19 11:51
【摘要】：近年来,计算机病毒的防治受到专家、学者以及社会各界人士的广泛关注,并成为互联网信息安全领域最具挑战性和最难攻克的难题之一.深入了解计算机病毒的特点和传播规律,进而建立病毒传播模型可以有效预测和控制计算机病毒的传播,并对建设安全和谐的网络环境起到积极推动作用.主要研究成果如下:①基于用户是否会预先安装杀毒软件与其对病毒的危害意识强弱有关,从而对一类分段SIRS病毒传播模型进行改进.主要研究了新模型的两类平衡点(无毒平衡点和病毒平衡点)的稳定性.首先推导出系统平衡点的存在性条件.其次,通过求系统在平衡点处的Jacobi矩阵的特征值来判断平衡点的局部稳定性.然后,构造Lyapunov函数进一步证明平衡点的全局稳定性.最后,数值仿真验证系统的平衡点是全局稳定的.②基于杀毒软件的杀毒能力与杀毒软件的成本有关,提出了一个分段SIQRS计算机病毒传播模型.主要研究了该模型的两类平衡点的稳定性.首先推导出系统的基本再生数和平衡点的存在性条件.其次,借助Routh-Hurwitz判别法和中心流形定理证明平衡点的局部稳定性.接着,构造Lyapunov函数并根据LaSalle不变原理证明平衡点的全局稳定性.然后,数值仿真验证结论的正确性.最后,讨论了系统的参数对基本再生数的影响,从而提出了三种有效的防御措施.
[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.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
[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.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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