STM Article Repository

This chapter is devoted to stability investigation of two mathematical models of rumor and information spreading. The mathematical model of rumor spreading is described by a system of four nonlinear differential equations, the nonlinear discrete-time model of information dissemination is described by a system of three difference equations. Equilibria of each system are defined and it is supposed that the considered model is influenced by stochastic perturbations of the different types that are proportional to the deviation of the system state from one of its equilibrium. Sufficient conditions of stability in probability for each from the equilibria of the considered model are obtained via the Routh-Hurwitz criterion, the Lyapunov functions method and the method of linear matrix inequalities (LMIs). The obtained results are illustrated by numerical analysis of appropriate LMIs via MATLAB and numerical simulations of solutions of the considered system of stochastic differential or difference equations. An unsolved problem is proposed to continue the presented investigations. The research method used here can be applied to investigate many other various applications for similar nonlinear mathematical models with an order of nonlinearity higher than one.