Hopf Bifurcation Research of University Network Public Opinion Propagation Model with Time Delay

Abstract

The dissemination of online public opinion in universities has always been a hot topic of concern, mainly revolving around issues such as academic misconduct, ethical conduct of faculty and staff, and campus safety, which are fermenting and spreading within the scope of universities. Strengthening the management of online public opinion in universities, studying the dissemination patterns and development trends of public opinion and rumors, and guiding college students to maintain a firm stance and distinguish right from wrong are of great significance. This article investigates the dynamic behavior of a university network public opinion dissemination model with a time delay. Firstly, the conditions for the existence of a positive equilibrium point in the model were discussed, and the local stability of the equilibrium point was analyzed. Applying the central manifold theorem and regularization theory, the study examined the sufficient conditions for Hopf bifurcation at this equilibrium point. It also discussed the stability and directionality of the periodic solution resulting from the bifurcation. Finally, the theoretical results were validated through numerical simulation, and the conclusions drawn have practical application value, providing a scientific basis for formulating strategies to control the spread of rumors.