Stability and bifurcation analysis in a delayed reaction-diffusion malware propagation model
Stability and bifurcation analysis in a delayed reaction-diffusion malware propagation model
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DOI：
10.1016/j.camwa.2015.02.004
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
Linhe Zhu;Hongyong Zhao;Xiaoming Wang
中科院分区：
文献类型：
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作者：
Linhe Zhu;Hongyong Zhao;Xiaoming Wang
由于传感器、无线通信和网络以及信号处理等方面的技术进步，移动无线传感器网络(MWSN)已经成为一个热门的研究领域。设想了许多应用，包括环境监测、战场监视和城市搜索和救援，特别是在危险情况下。然而，由于MWSN的大规模特性，它可能容易受到恶意干扰。当受污染的节点与其邻居通信时，恶意软件的多个副本被传输到其邻居，这可能会破坏、阻止常规通信，甚至破坏常规数据包的完整性。对恶意软件传播随时间的空间分布进行建模是预测恶意软件在MWSN中传播趋势的第一步。基于移动无线传感器网络中的反应扩散方程，提出了一种新的具有离散时延的无线恶意软件传播模型，并对其动态行为进行了研究。通过分析模型平衡点的稳定性和Hopf分支，寻找导致恶意软件传播消失或继续的充分条件。此外，我们还证明了该模型的振荡是通过在Hopf分岔点处的定常解的失稳来实现的。应用规范形法和中心流形定理，得到了判定分叉周期振动稳定性的公式。最后，我们在大规模的MWSN上进行了大量的仿真来评估所提出的模型。数值实验表明，恶意软件在MWSNs中传播的时空动态特性与分组传输速率、通信距离和节点的移动行为密切相关。
Mobile wireless sensor networks (MWSNs) have become an area of intense research activity due to technical advances in sensors, wireless communications and networking, and signal processing. Many applications, including environment monitoring, battlefield surveillance, and urban search and rescue especially in hazardous situations, are envisaged. However, MWSNs may be vulnerable to malicious interference because of the large-scale characteristics. When a contaminated node communications with its neighbors, multiple copies of the malware are transmitted to its neighbors, which may destroy, block regular communications, or even damage the integrity of regular data packets. Modeling spatial distribution of malware propagation over time is the first step to predict the trend of malware propagation in MWSNs. We propose a novel wireless malware propagation model with the discrete time delay based on reaction–diffusion equations in mobile wireless sensor networks, and study its dynamic behaviors. By analyzing the stability and Hopf bifurcation of the equilibrium of our model, we search for the sufficient conditions, which leads to the malware propagation disappears or continues. Furthermore, we demonstrate that oscillations in this model occur through the destabilization of the stationary solution at a Hopf bifurcation point. And formulas for determining the stability of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidence shows that the spatial–temporal dynamic characteristics of malware propagation in MWSNs are closely related to the packet transmission rate, the communication rang and the mobile behavior of nodes.