Dynamics of a reaction-diffusion rumor propagation model with non-smooth control - Ke, Yue; Zhu, Linhe; Wu, Peng; Shi, Lei (Applied mathematics and computation, 2022)
•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.