Stability under stochastic perturbation of solutions of mathematical models of information spreading process with external control

Abstract

In this paper mathematical model of spreading any number of information types with external influences is considered. The model takes the form of n (number of information channels) non-linear Ito stochastic differential equations. Conditions for asymptotic stability in quadratic average in first-approximation of the special points are considered for general stationary model and special case with non-stationary parameters. The results of example are presented for the special case of the base model with stationary parameters.

Dynamics analysis and forecast of number of individuals with stress syndrome under uncertainties

“…In this article, we focus on the estimation and forecasting of parameters in a model that reflects the dynamics of individuals experiencing stress syndrome in conditions of uncertainty, based on methods and mathematical models of population dynamics (Nakonechnyi, Marzenyuk, 2004), (Nakonechnyi, Shevchuk, 2018), (Nakonechnyi, et. al., 2020).…”

Analysis the solutions of the differential non-linear equations describing the information spreading process with jump discontinuity

“…Works [6] are devoted to analysis of solution oh this model (1), (2) with stationary parameters and the special type of u k (t), k = 1, N , t ∈ (t 0 , T ). Conditions of existence of range of first-approximation stability of the solutions are considered in [7], [8]. A separate practical-important case of the model (1), (2) is the equations with jumps discontinuity that are appropriate to be modeled as pulsed perturbations (for example, [9]).…”