Stability analysis of stochastic pantograph multi-group models with dispersal driven by G-Brownian motion

摘要

In this work, we discuss the stability of stochastic pantograph multi-group models with dispersal perturbed by G-Brownian motion (G-SPMGMs, for short) with general decay rate, which includes polynomial stability, exponential stability, and logarithmic stability as special cases. With the help of G-vertex-Lyapunov functions, G-stochastic analysis technique and graph-theory on multi-digraph, sufficient criteria are obtained for the stability of G-SPMGMs. An application to a class of stochastic coupled pantograph oscillators with G-Brownian motion perturbation and an example are given to demonstrate the obtained results.