A graph‐theoretic approach to stability of neutral stochastic coupled oscillators network with time‐varying delayed coupling

Abstract

In this paper, a graph-theoretic approach for checking exponential stability of the system described by neutral stochastic coupled oscillators network with time-varying delayed coupling is obtained. Based on graph theory and Lyapunov stability theory, delay-dependent criteria are deduced to ensure moment exponential stability and almost sure exponential stability of the addressed system, respectively. These criteria can show how coupling topology, time delays, and stochastic perturbations affect exponential stability of such oscillators network. This method may also be applied to other neutral stochastic coupled systems with time delays. Finally, numerical simulations are presented to show the effectiveness of theoretical results.

Graph-Theoretic Approach to Exponential Stability of Delayed Coupled Systems on Networks under Periodically Intermittent Control

“…In order to further study, we need to prepare a definition about k-th vertex-Lyapunov function following [30] and two basic assumptions first.…”

Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach

“…Utilizing the achievements of the pioneering works, few researchers have initiated their work and apply this approach. For example, in [30], boundedness of the stochastic van der Pol oscillators was studied, in [32], boundedness of the stochastic differential equations were studied, in [33], stability of the neutral networks was studied. In [31], the boundedness of stochastic Cohen-Grossberg neural networks was studied by using M-matrix theory, Lyapunov and graph theory.…”

On input-to-state stability for stochastic coupled control systems on networks

“…By applying Kirchhoff's matrix tree theorem in graph theory, a systematic approach was given to constructed Lyapunov function for coupled systems on networks. This technology has been successfully employed in the global stability for many mathematic models on networks, such as, coupled oscillators model [29,30], multi-group model [31,32], and neural networks [33], etc. Moreover, this technology was also extended to many different systems, such as stochastic system [11,34,35], discrete-time system [36,37], and delay system [29,37,38].…”