Stability and boundedness analysis of stochastic coupled systems with pantograph delay

Abstract

Coupled systems on the network play important role in many social and natural fields. To consider the effects of delays shown as pantograph delay, in this work, we deal with a class of stochastic coupled systems with pantograph delay (PSCSs, in short). The main aims include the exponential stability and boundedness of the trivial solution for PSCSs are established. By means of graph theory, Lyapunov method and stochastic analysis technique, we establish the p-th moment exponential stability and p-th moment exponential ultimate boundedness conditions for PSCSs. Two examples are given to illustrate the effectiveness and feasibility of the theoretical results.