Inter-layer Synchronization In Two-layer Networks With Impulsive Effect

In recent years,complex networks has been widely used in many research fields,such as the World Wide Web,neural networks,social networks,smart grids,etc.The research on complex dynamical networks and synchronization in networks is a hot topic that many researchers are keen on.Most of these studies are focused on one-layer network,and the research on one-layer network is tended to mature.However,due to the complexity and diversity of real networks,more and more scholars put research directions on the research of two-layer networks and even multi-layer networks.Establishing such a network model can describe the real network more accurately.Inter-layer synchronization of two-layer networks is a relatively new research direction.Unlike other network research objects,it mainly studies the inter-layer synchronization.In the process of studying the inter-layer synchronization,we find that there may be an interaction relationship between the two layers of networks,namely impulse coupling.Therefore,under the influence of impulse coupling,we further explore it.Firstly,we consider the two-layer dynamic network with the same topology in Chapter 2.We derive the sufficient conditions with respect to impulsive gains and intervals for achieving synchronization according to Lyapunov function method and mathematical analysis technique.According to the synchronization conditions,we can calculate the required values of the impulsive gains and impulsive intervals for achieving synchronization.Finally,we perform several numerical simulations on the two-layer networks coupled with Chen systems to verify the theoretical results.Secondly,we consider the two-layer dynamic network with coupling delay and the same topol-ogy in Chapter 2.The inter-couplings between layers are also impulsive.We provide the synchro-nization criteria according to Lyapunov function method and mathematical analysis technique,which are independent with coupling delay.For any given two-layers network,we can easily es-timate the impulsive gains and impulsive intervals from the criteria.We perform two numerical simulations on the two-layer networks coupled with Chen systems to verify the theoretical results as well.Finally,we conclude this thesis and propose some issues worth considering in future research.