The stability analysis of stochastic opinion dynamics systems with multiplicative noise and time delays

This paper studies the stochastic stability of opinion formation systems under both non‐time delay and time delay. Individuals whose opinions are affected by multiplicative noise are considered. Subsequently, a stochastic opinion formation model on coopetitive social networks which take both multiplicative noise and time delay into consideration and give the analysis of stochastic stability is introduced. When the continuous‐time system of opinion evolution is disturbed by stochastic multiplicative noise, the stability of the stochastic opinion formation system is dependent on the noise intensity and the topology structure. When the continuous‐time system of opinion dynamic is disturbed by time delay and multiplicative noise, the bounds of the noise intensity and time delay ensure the stochastic stability of the above system. Finally, numerical simulations are given to illustrate the above theoretical results.