Research On The Propagation And Control Problem Of Stochastic Rumor

Rumors have existed since ancient times and were first spread by word of mouth.With the rapid development of Internet technology,rumors have emerged in a variety of channels and modes of transmission,spreading faster and more widely.The spread and proliferation of rumors not only endangers human life,but also has a negative impact on the stability of society.In this regard,it is important to investigate the mechanism of the spread of rumors and adopt effective control strategies to reduce the negative effects of rumors.The thesis mainly refers to the classical DK model of rumor propagation,but also takes into account individual psychological factors,individual reaction time and external random interference,and proposes a new and more realistic model of stochastic rumor propagation.Finally,on the basis of this model,the control strategies of "education mechanism" and "refutation mechanism" are added,and the optimal control strategy for rumor propagation is explored in three ways: continuous control,pulse discrete control and event-triggered pulse control.The following results are obtained:(1)The dynamic evolution of the stochastic rumor propagation model is investigated,and the sufficient conditions for the near-optimal control of the "education mechanism" and "refutation mechanism" under continuous control are explored.The validity of the theoretical analysis and the existence of near-optimal solutions are confirmed by numerical simulations.The conclusions show that the dynamic behavior of rumor propagation is significantly related to the propagation rate,time lag and white noise intensity,and that reducing the propagation rate or extending the time lag can reduce the size of rumor propagation.Under the continuous control approach,both control strategies have good inhibitory effects on rumor propagation.(2)On the basis of the stochastic rumor propagation model,the control strategies of "education mechanism" and " refutation mechanism" in the form of pulses are proposed,and the dynamic evolution law of the stochastic rumor propagation model with pulses is studied.The problem of optimal control of pulses is studied with the objective function of minimizing the spread scale and cost of rumor control,and the optimal control solution is derived.The numerical simulation shows that the optimal pulse control strategy can effectively control the spread of rumors,and the optimal control strength of the "education mechanism" and " refutation mechanism" should be dynamically adjusted according to the different scenarios of rumor spread.(3)Based on the event-triggered pulse function,a stochastic rumor propagation model is investigated,and a control strategy in the form of an event-triggered " refutation mechanism" is introduced to dynamically select the control time node according to the scale of rumor propagation.In addition,a particle swarm optimization algorithm is used to explore the optimal event-triggered impulse control strategy under different propagation scenarios.The results show that the control strength,control time nodes and control frequency(i.e.the event trigger pulse function)need to be adjusted dynamically under different propagation levels.In the process of rumor control,officials should grasp the right timing and control propagation at a reasonable point in time.