Abstract:This paper studies the dynamic behaviour of a computer worm system under a discontinuous control strategy. Some conditions for globally asymptotically stable solutions of the discontinuous system are obtained by using the Bendixson-Dulac theorem, Green's formula, and the Lyapunov function. It is found that the solutions of the controlled computer worm system can converge to either of two local equilibrium points or the sliding equilibrium point on the discontinuous surface. It is shown that a threshold control strategy can effectively control the spread of computer viruses. The research results may be applicable to control other types of virus systems.

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中文翻译：

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受控不连续计算机蠕虫系统的动力学

摘要：本文研究了不连续控制策略下计算机蠕虫系统的动态行为。通过使用Bendixson-Dulac定理，Green公式和Lyapunov函数，获得了不连续系统全局渐近稳定解的一些条件。发现受控计算机蠕虫系统的解可以收敛到不连续表面上的两个局部平衡点或滑动平衡点。结果表明，阈值控制策略可以有效地控制计算机病毒的传播。研究结果可能适用于控制其他类型的病毒系统。

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