A time-delay rumor propagation model incorporating the generalized Hawk–Dove Game and the transient forgetting mechanism

This paper introduces the influence of external environmental factors and constructs a generalized Hawk–Dove Game model to systematically explore the dynamic evolutionary patterns between aggressors and conservatives in the population. Based on this, a rumor propagation model with whistleblowers and transient forgetters is further established. This model considers the characteristic that transient forgetters are easily influenced by the bandwagon effect when recalling rumors and incorporates the time-delay effect. In addition to deriving the threshold for rumor propagation, this paper further analyzes the local and global equilibria of the model, as well as its Hopf bifurcation behavior. Finally, numerical simulations validate the theoretical results and fit the model to a practical example. The results show that when aggressors interact, if the action cost exceeds the expected benefit, the population tends to adopt a conservative strategy. Further analysis reveals that this scenario effectively suppresses rumor propagation. Additionally, the number of transient forgetters significantly impacts the scale of both whistleblowers and propagators. Comprehensive consideration of public opinion tendencies and time-delay effect is essential for more effective rumor control.