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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (4): 647-660.doi: 10.3969/j.issn.1005-3085.2023.04.010

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一类时滞分数阶计算机病毒模型的Hopf分岔控制研究

高燕鑫1,2,  石剑平1   

  1. 1. 昆明理工大学理学院，昆明  650500;
    2. 山西能源学院强基学院，太原 030604
  • 收稿日期:2020-12-12 接受日期:2021-07-20 出版日期:2023-08-15 发布日期:2023-10-15
  • 基金资助:
    国家自然科学基金(11561034; 11761040)；云南省教育厅科学研究基金(2017ZZX133).

Hopf Bifurcation Control Analysis of a Time-delay Fractional Computer Virus Model

GAO Yanxin1,2,  SHI Jianping1   

  1. 1. School of Science, Kunming University of Science and Technology, Kunming 650500;
    2. College of Basic Courses, Shanxi Institute of Energy, Taiyan 030604
  • Received:2020-12-12 Accepted:2021-07-20 Online:2023-08-15 Published:2023-10-15
  • Supported by:
    The National Natural Science Foundation of China (11561034; 11761040); the Scientific Research Foundation of Yunnan Education Department (2017ZZX133).

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摘要：

研究了一类时滞分数阶计算机病毒模型Hopf分岔的控制问题。在非受控系统的第一个方程中引入周期脉冲时滞反馈控制器，采用半解析半数值的方法证明了受控系统与其线性化平均系统在一定意义下的等效性，并以此作为理论基础，采用线性化方法和分数阶Laplace变换推导受控系统发生Hopf分岔的临界值，得到系统的稳定域范围以及稳定域随控制器参数的变化情况。结果说明通过调节增益参数值，可有效的延迟系统Hopf分岔的发生。最后，通过恰当的数值模拟验证了理论分析的正确性和可行性，并对比了不同控制增益参数对系统稳定域的影响。

关键词: 分数阶, 时滞, Hopf分岔, 计算机病毒模型, 周期脉冲控制

Abstract:

The control problem of Hopf bifurcation for a time-delayed fractional computer virus model is considered. A periodic pulse delay feedback controller is introduced into the first equation of the uncontrolled system. The semi-analytical and semi-numerical method is used to prove the equivalence between the controlled system and its linearized average system. From this theoretical basis, the critical value of Hopf bifurcation in the controlled system is derived by the linearization method and the fractional Laplace transform, and the range of the stability domain and the variation of the stability domain with the controller parameters are obtained. The results show that the Hopf bifurcation of the system can be effectively delayed by adjusting the gain parameter value. Finally, the correctness and feasibility of the theoretical analysis are verified by appropriate numerical simulation, and the influence of different control gain parameters on the system stability domain is compared.

Key words: fractional-order, time-delay, Hopf bifurcation, computer virus system, periodic pulse control

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