Stability of highly nonlinear impulsive coupled networks with multiple time delays

The stability of highly nonlinear impulsive coupled networks (HNICNs) with multiple time delays is investigated in this paper. Impulsive differential inequalities are important research tools to investigate the stability of impulsive systems. However, most of the existing impulsive differential inequalities are linear, so they are no longer applicable when highly nonlinear factors are considered in impulsive coupled networks. This makes our research difficult. To address this problem, a novel impulsive differential inequality is established, which incorporates both high nonlinearity and multiple time delays. This inequality provides a powerful tool for investigating the stability of HNICNs with multiple time delays. Then, using the Lyapunov method and graph theory, the main results are proposed to guarantee the stability of HNICNs with multiple time delays. Next, our results can be applied to derive the stability of modified FitzHugh-Nagumo circuits and modified Van der Pol-duffing oscillators. Ultimately, numerical simulations are given to verify the effectiveness of theoretical results.