Second-order synchronization of two nonlinear coupled networks with heterogeneous nonlinear dynamics and time-varying delays

This paper addresses the second-order synchronization between two nonlinear coupled networks with heterogeneous nonlinear dynamics and time-varying delays. In order to obtain second-order synchronization, a controller and adaptive laws are designed. By constructing the Lyapunov function, it is proved that the position and the velocity of two heterogeneous nonlinear coupled networks with time-varying delays are asymptotically stable under certain conditions. Finally, some numerical simulations are given to verify the analytical results.