Weighted exponential stability of stochastic coupled systems on networks with delay driven by <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula>-Brownian motion

Abstract

This paper investigates the issue of weighted exponentially input to state stability (EISS, in short) of stochastic coupled systems on networks with time-varying delay driven by G-Brownian motion (G-SCSND, in short). Combining with inequality technique, kth vertex-Lyapunov functions and graphtheory, we establish the weighted EISS for G-SCSND. An application to the EISS for a class of stochastic coupled oscillators networks with control inputs driven by G-Brownian motion and an example are provided to illustrate the effectiveness of the obtained theory.

The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise

“…In recent years, stability of stochastic ordinary and stochastic partial differential equations, providing relevant information on the long time behavior of the solutions of such equations, has received much attention (see, e.g., 28,34,35,37,46,51,55,58,61 ). Hölder continuous paths approach has been used in 13,14,25 to study the exponential stability of a ordinary or partial differential equation driven by fractional Brownian motion with Hurst parameter H ∈ (1/2, 1).…”