Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

Stability and bifurcation for a stochastic differential algebraic Holling-Ⅱ predator-prey model with nonlinear harvesting and delay

In this paper,a stochastic delayed differential algebraic predator-prey model with Michaelis-Menten-type prey harvesting is proposed.Due to the influence of gestation delay and stochastic fluctuations,the proposed model displays a complex dynamics.Criteria on the local stability of the interior equilibrium are established,and the effect of gestation delay on the model dynamics is discussed.Taking the gestation delay and economic profit as bifurcation parameters,Hopf bifurcation and singularity induced bifurcation can occur as they cross through some critical values,respectively.Moreover,the solution of the model will blow up in a limited time when delay τ>τ0.Then,we calculate the fluctuation intensity of the stochastic fluctuations by Fourier transform method,which is the key to illustrate the effect of stochastic fluctuations.Finally,we demonstrate our theoretical results by numerical simulations.