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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,6,30]]},"abstract":"<jats:p> Rumors may cause serious harm to social productivity and life. Studying the dynamics of rumor propagation can help provide corresponding countermeasures to control communication effectively. Based on the classic [Formula: see text] infectious disease model, this paper studies a rumor spreading model with a time delay caused by communication delay between rumor communicators and nonsmooth threshold propagation function in reality. In this model, we solve non-negative equilibrium points firstly. By analyzing the characteristic equations of smooth and nonsmooth rumor systems, we establish local stability at non-negative equilibrium points and find the existence of Hopf bifurcation from two aspects of diffusion coefficient and delay, respectively. 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