Spreading dynamics of a preferential information model with hesitation psychology on scale-free networks
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(2019) 2019:279
RESEARCH
Open Access
Spreading dynamics of a preferential information model with hesitation psychology on scale-free networks Xiongding Liu1,2 , Tao Li1,2* , Xinming Cheng3 , Wenjin Liu1,2 and Hao Xu1,2 *
Correspondence: [email protected] 1 National Demonstration Center for Experimental Electrical and Electronic Education, Yangtze University, Jingzhou, P.R. China 2 School of Electronics and Information, Yangtze University, Jingzhou, P.R. China Full list of author information is available at the end of the article
Abstract Considering the influence of the preferential degree, the hesitation psychology of customers and the heterogeneity of underlying networks in preferential information spreading, we propose a novel model called AHFB (adherent–hesitator–forwarder– beneficiary) model to illustrate the dynamic behaviors of preferential information spreading on scale-free networks. The mean-field theory is adopted to describe the formulas of AHFB model. To begin with, we analyze the spreading dynamics of preferential information. Then we determine the basic reproductive number and equilibria by the next generation matrix method. The relationship among the basic reproductive number, preferential degree, and hesitation parameter is also analyzed. In addition, the globally asymptotical stability of information-eliminate equilibrium and the permanence of the preferential information spreading are proved in detail. Furthermore, a preferential information competition model is proposed, and the corresponding dynamic behaviors are studied. We have found that under certain conditions, a greater competitive advantage can be achieved by improving a certain range of preferential strengths. Numerical simulations are also presented to verify and extend theoretical results. Keywords: Attractivity parameter; Preferential information spread model; Heterogeneity; Scale-free networks; Hesitation psychology
1 Introduction With the continuous prosperity of mobile Internet technology and the appearance of the 5G, e-commerce technology is rapidly developing and multifarious applications are emerging. As a kind of Internet networks, e-commerce networks not only play an important role in spreading information and promoting communication, but also penetrate people’s daily life, such as convenient shopping, mobile payment [1–3]. In most instances, e-commerce networks provide businesses with a platform to release preferential information and display merchandises [4, 5]. In order to obtain discounts or small gifts from the store during the shopping process, customers need to forward the corresponding preferential information [6]. Therefore, the preferential information will be spread widely. In the field of complex networks, researchers have made some achievements in information spreading [7–14] and network control [15–19]. Based on the characteristics of network structure, the effects of different network topologies, such as small world net© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Att
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