Stochastic Stabilization of Dual-Layer Rumor Propagation Model with Multiple Channels and Rumor-Detection Mechanism.

With the development of information technology, individuals are able to receive rumor information through various channels and subsequently act based on their own perceptions. The significance of the disparity between media and individual cognition in the propagation of rumors cannot be underestimated. In this paper, we establish a dual-layer rumor propagation model considering the differences in individual cognition to study the propagation behavior of rumors in multiple channels. Firstly, we obtain the threshold for rumor disappearance or persistence by solving the equilibrium points and their stability. The threshold is related to the number of media outlets and the number of rumor debunkers. Moreover, we have innovatively designed a class of non-periodic intermittent noise stabilization methods to suppress rumor propagation. This method can effectively control rumor propagation based on a flexible control scheme, and we provide specific expressions for the control intensity. Finally, we have validated the accuracy of the theoretical proofs through experimental simulations.

Global stability of the boundary solution of a nonautonomous predator-prey system with Beddington-DeAngelis functional response.

In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results.