Dynamics of a reaction-diffusion rumor propagation model with non-smooth control

•This paper presents a novel non-smooth rumor spreading model.•Complex dynamics are studied by using the theory of partial differential equations.•Nonlinear control function is adopted in modeling and we have proved its effectiveness. To reflect the government and media refutation to rumor propagati...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 435; p. 127478
Main Authors: Ke, Yue, Zhu, Linhe, Wu, Peng, Shi, Lei
Format: Journal Article
Language:English
Published: Elsevier Inc 15.12.2022
Subjects:
Bifurcation theory
Non-smooth system
Reaction-diffusion model
Rumor propagation
Stability analysis
Reaction-diffusion model
Bifurcation theory
Stability analysis
Non-smooth system
Rumor propagation
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:•This paper presents a novel non-smooth rumor spreading model.•Complex dynamics are studied by using the theory of partial differential equations.•Nonlinear control function is adopted in modeling and we have proved its effectiveness. To reflect the government and media refutation to rumor propagation, we have established a reaction-diffusion rumor propagation model by considering a non-smooth control function. Firstly, we obtain the rumor propagation threshold according to the next generation matrix theory, prove the existence and uniqueness of solution and discuss the existence of the equilibrium points. Secondly, we discuss the stability of the equilibrium points with the impact of the spatial diffusion. Thirdly, the conditions for spatially homogeneous and discontinuous Hopf bifurcation are presented. Finally, several numerical simulations are given to show the possible impact, and the factors affecting rumor propagation are theoretically analyzed, which proves the validity of the theoretical analysis.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2022.127478