Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Changjin Xu,Peiluan Li,Maoxin Liao

doi:10.1155/2019/7057052

Abstract

In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security.

Highlights

Nowadays, social networks are important platforms for disseminating information and building relationship
Deng et al.[1] considered the mobility-based clustering protocol of wireless sensor networks, Liu et al [2] focused on the design and statistical analysis of a new chaotic block cipher for wireless sensor networks, Wang and Tseng [3] discussed the distributed deployment schemes for mobile wireless sensor networks, and Kulkarni and Zambare [4] studied the impact of Houseplants in purification of environment using wireless sensor network
We investigate the Hopf bifurcation of delayed malware propagation model

Summary

Introduction

Social networks are important platforms for disseminating information and building relationship. Different from the classical approaches of communication, social networks have fast speed of information propagation and diffusion. Social networks have important effect on commercial negotiations, social connections, and information-sharing activities. Malware, which widely appears in the Internet, will cause some serious security risks of networks such as network paralysis, instability of society, loss of secret key, and personal information leakage. Their research shows that interpretation of malware parameters and prediction of the evolution of future malware outbreaks play an important role in ensuring user safety. Signes Pont et al [6] modelled the malware propagation in mobile computer devices. Hosseini and Azgomi [7] considered the Discrete Dynamics in Nature and Society stability of an SEIRS-QV malware propagation model in heterogeneous networks. One can see [7,8,9,10,11]

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Conclusion