Research Of Adaptive Synchronous Dynamics On Duplex Complex Networks

In real world,the nodal states of a network sometimes change through time.So it is important to investigate diffusion and synchronization processes on single-layer and multilayer networks.Most research about the dynamical processes on complex networks is based on a stationary nodal coupling.In order to model the real systems,in which the nodal couplings are varying with respect to time,this thesis focus on exploring adaptive diffusion and synchronization processes on single-layer and multilayer networks by mean-field method,nonlinear dynamics theory and statistical mechanics.The main results are shown as follows:1.Constructing an adaptive diffusion model of time varying local information on networks,which is based on the fact that the nodal couplings in a real network sometimes change with respect to time.Using different kinds of technics,like numerical simulation,to investigate the impact of network topologies on diffusion processes.Meanwhile,during the adaptive diffusion processes,nodes with smaller degrees are more likely to change their states and reach larger values,while those with larger degrees tend to stick to their original states.Furthermore,this thesis introduce state entropy to analyze the thermodynamic mechanism of the diffusion process,and find that the adaptive diffusion process is a non-spontaneous process.2.To explore the influence of duplex spacial networks’ topology on phase synchronization,this part construct a Kuramoto phase synchronization model on duplex spacial networks.Using numerical simulation to investigate the impact of single-layer spacial network’s topology on phase synchronization,and finding that more stochastic structure is more beneficial for phase synchronization.Meanwhile,for duplex networks,synchronization will emerge with strong enough inter-layer and intra-layer couplings.Furthermore,because of the importance of inter-layer couplings,the inter-layer synchronization can exist independently and always occurs firstly.For single-layer networks,nodes with large degree are more easily to reach synchronous state.While for duplex networks,with the existence of inter-layer couplings,the impact of degree on synchronization may be weaken by inter-layer couplings,which further illustrates the importance of inter-layer couplings.3.For frequency synchronization,this part finds a kind of condensed synchronous orbits phenomenon on single-layer and duplex networks through statistical mechanics analysis and numerical simulation,where the distribution of synchronous orbits follows a Gaussian form.In addition,this thesis investigates phase synchronization on single-layer and duplex networks with different distributions of initial frequency values.The thesis finds that normally distributed initial frequency values with low variances are more beneficial for phase synchronization,and more separately distributed initial frequency values can hinder the synchronization process.In the end,this thesis investigates the influence of one layer’s initial frequencies on the other layer’s phase synchronization through inter-layer couplings.Interestingly,one layer’s initial frequency values with highly condensed distribution can greatly improve phase synchronization on the other layer.