Stability Analysis Of Two Classes Of Complex Network Models Under The G-Framework

This paper investigates the issue of stability of two classes of complex network models under the G-framework.This work is divided into two sections.In the first section,we consider the following stochastic coupled systems on networks with time-varying delay driven by G-Brownian motion(G-SCSND,in short)based on a digraph g with N(N? 2)vertices.(?)or its' compact form (?)(2)where B(·)is a G-Brownian motion,(B)(·)is the corresponding quadratic variation pro-cess,(?)Rmk are continuously activation functions,(?)are continuous functions.?(t)is the time-varying delay with 0??(t)??,?(t)??<1.The initial value ?={?(s);-??s?0)} is an F0-progressively process,(?)is the family of continuous functions ? from(?)to Rm with the norm (?) and random variable ? such that E||?|p<? for any p>2.Combining with inequality tech-nique,kth vertex-Lyapunov functions and graph-theory,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.In section 2.we study the stabilization for stochastic differential equations driven by G-Brownian motion(G-SDEs,in short)based on G-Lyapunov function and aperiodically adaptive intermittent controller.More specifically,if the following G-SDEs is unstable(?)we design a controller U(t)embedded into the drift coefficient such that the controlled system to become stable.We further consider the unstable stochastic Cohen-Grossberg neural networks driven by G-Brownian motion(G-SCGNNs,in short)with the following form(?)is the connection weight matrix,(?)Here,n corresponds to the number of units in a neural network,xi(t)denotes the state variable of cell i at time t,ci(·)is an amplification function,di(·)is an appropriately behaved function,fi(·)denotes the activation function,aij denotes the strengths of connectivity between cell i and j.