Abstract
This paper analyzes the diffusion behavior of the suspicious and the infected cabins in cyberspace by establishing a rumor propagation reaction–diffusion model with Allee effect and time delay. The Turing instability conditions of the system are emphatically studied. After considering the effect of time delay on the rumor propagation system, we have studied the correlation between the stability of the system under the influence of small time delay and the homogeneous system near the equilibrium point; the critical condition of the delay-induced spatial instability is given as well. Then, we prove the existence of Hopf bifurcation induced by time delay in some cases. Further considering the possibility of diffusion coefficient changing with time, the critical parameter curves of stability and instability of approximate systems are given by means of Floquet theory, and the necessary conditions of Turing instability of periodic coefficient are studied. In the numerical simulations, we find that the variation in diffusion coefficient and time delay will change the pattern type, and the periodical diffusion behavior will affect the arrangement of the crowd gathering area in the pattern.
Highlights
Nowadays, social network environment is characterized by fast information dissemination speed and low access cost, making it a stepping stone for false information and influencing public opinion1
After considering the delay effect of rumor propagation systems, we have studied the correlation between the stability of the system under the influence of small time delay and the homogeneous system near the equilibrium point, and the critical condition of the delay-induced spatial instability is given
We find that the variation of diffusion coefficient will change the pattern type, and the periodical diffusion behavior will affect the arrangement of the crowd gathering area in the pattern
Summary
Social network environment is characterized by fast information dissemination speed and low access cost, making it a stepping stone for false information and influencing public opinion. Due to the high correlation between epidemic transmission and related information in practice and the similarity of transmission process, some work have tried to establish the coupling model of information transmission and disease transmission.. Due to the high correlation between epidemic transmission and related information in practice and the similarity of transmission process, some work have tried to establish the coupling model of information transmission and disease transmission.14–16 It reveals the mechanism of the interaction between disease and related consciousness. These works reflect the important potential practical value of the research on the dynamics of information and rumor propagation. We put forward the conclusion of our work in the sixth section
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