Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 26, Issue 6, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127416501017
Keywords
Rumor propagation; stability; traveling wave solution; Hopf bifurcation; time delay
Funding
- National Natural Science Foundation of China [61174155, 11571170]
- Qing Lan Project of Jiangsu
- Funding of Jiangsu Innovation Program for Graduate Education [KY ZZ15_0091]
- Fundamental Research Funds for the Central Universities
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The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder's fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.
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