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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 610382, 12 pages
http://dx.doi.org/10.1155/2014/610382
Research Article

Cooperative and Competitive Dynamics Model for Information Propagation in Online Social Networks

1School of Economics and Management, Yanshan University, Qinhuangdao 066004, China
2Department of Computer Science, University of Brasilia, 70910-900 Brasilia, DF, Brazil

Received 1 May 2014; Revised 23 June 2014; Accepted 23 June 2014; Published 13 July 2014

Academic Editor: Francisco J. Marcellán

Copyright © 2014 Yaming Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Traditional empirical models of propagation consider individual contagion as an independent process, thus spreading in isolation manner. In this paper, we study how different contagions interact with each other as they spread through the network in order to propose an alternative dynamics model for information propagation. The proposed model is a novel combination of Lotka-Volterra cooperative model and competitive model. It is assumed that the interaction of one message on another is flexible instead of always negative. We prove that the impact of competition depends on the critical speed of the messages. By analyzing the differential equations, one or two stable equilibrium points can be found under certain conditions. Simulation results not only show the correctness of our theoretical analyses but also provide a more attractive conclusion. Different types of messages could coexist in the condition of high critical speed and intense competitive environment, or vice versa. The messages will benefit from the high critical speed when they are both competitive, and adopting a Tit-for-Tat strategy is necessary during the process of information propagation.