一类具有非线性发生率的无线传感网络蠕虫传播模型的延迟动力学行为

研究了一类具有不同发生率的无线传感网络蠕虫传播模型的延迟动力学行为。由于在监测节点隔离不稳定节点需要消耗一定的时间，在模型中考虑了处理时滞。通过分析相应特征方程根的分布情况，得到了平衡点存在性、模型局部稳定性和Hopf分岔存在的充分性条件。通过构造合适的李雅普诺夫函数，证明了蠕虫病毒平衡点的全局稳定性。数值仿真实验验证了理论分析结果的正确性。仿真结果表明，当处理时滞的值越过关键值时，网络中的蠕虫传播将失去控制，发现无线传感网络的覆盖范围是控制蠕虫传播和保证无线传感网络安全最为重要的因素之一。并通过仿真发现消除模型混沌状态的一些关键参数，其中非线性发生率βSII+1是控制蠕虫病毒传播、保证无线传感网络安全的最佳选择。

Delay dynamics of worm propagation model with non-linear incidence rates in wireless sensor network

In this paper, delay dynamics of a worm propagation model has been investigated with different incidence rates in wireless sensor network. Processing time delay occurs in the proposed model due to time consumed during monitoring the erratic behaviors of the nodes and isolating it from the network. Sufficient conditions for the existence of equilibrium points, stability analysis and Hopf bifurcation of the system are derived by analyzing distribution of roots of an associated characteristic equation. Global stability for worm-induced equilibrium is derived by constructing a suitable Lyapunov function. To verify analytical results, numerical simulations are carried out. In the case that the processing time delay exceeds the critical value, the worms in the network is beyond the control. There are many significant features of wireless sensor networks, among them coverage area is the most effective factor with respect to worm control and security purposes. The value of some influential parameters of sensor network are carefully selected so that the oscillations can be reduced and removed from the network. According to comparative study of model systems, it can be concluded that the incidence rate βSII+1 is one of the best selection for worm control and security purposes in wireless sensor network.