Time-Delay Reaction-Diffusion Rumor Propagation Model with Saturation Control
Hopf bifurcation is a kind of simple but important dynamic bifurcation problem,which means that when the system parameter changes past the critical value,the equilibrium point changes from stable to unstable and a limit cycle is generated.Based on Hopf bifurcation,this paper proposes a time-delay reaction-diffusion rumor propagation model with saturated control,which better reflects the characteristics of rumor propagation in real life,and studies the Turing instability and Hopf bifur-cation.Meanwhile,the time delay is selected as the bifurcation parameter,and the analytic expression of the bifurcation threshold is given.Finally,the correctness of the theoretical results is verified by numerical simulation.The results show that both diffusion and time delay are the causes of the system instability.The traditional rumor propagation model only considers the time evolution,while the model depicts the traditional rumor propagation model from the two dimensions of time and space,making it more appropriate to reflect the law of rumor propagation in real life,and providing new ideas for the governance of rumor propagation.
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