The topological structure of a complex dynamical network plays a vital role in determining the network＇s evolutionary mecha- nisms and functional behaviors, thus recognizing and inferring the network structure is of ...The topological structure of a complex dynamical network plays a vital role in determining the network＇s evolutionary mecha- nisms and functional behaviors, thus recognizing and inferring the network structure is of both theoretical and practical signif- icance. Although various approaches have been proposed to estimate network topologies, many are not well established to the noisy nature of network dynamics and ubiquity of transmission delay among network individuals. This paper focuses on to- pology inference of uncertain complex dynamical networks. An auxiliary network is constructed and an adaptive scheme is proposed to track topological parameters. It is noteworthy that the considered network model is supposed to contain practical stochastic perturbations, and noisy observations are taken as control inputs of the constructed auxiliary network. In particular, the control technique can be further employed to locate hidden sources （or latent variables） in networks. Numerical examples are provided to illustrate the effectiveness of the proposed scheme. In addition, the impact of coupling strength and coupling delay on identification performance is assessed. The proposed scheme provides engineers with a convenient approach to infer topologies of general complex dynamical networks and locate hidden sources, and the detailed performance evaluation can further facilitate practical circuit design.展开更多
This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchron...This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchronization criteria for this kind of net works.The results provide an effective way to synchronize discrete-time complex networks by reducing control cost.Furthermore,these theoretical results are illustrated by a complex network via two kinds of pinning schemes.Numerical simulations verify the feasibil计y of the proposed methods.展开更多
Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper.The rewiring mechanisms are named as model-preserving rewiring(MPR), simply direct rewir...Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper.The rewiring mechanisms are named as model-preserving rewiring(MPR), simply direct rewiring(SDR), and degree-preserving rewiring(DPR), respectively. It is found that high switching frequencies will certainly enhance global synchronizability for WSWS duplex networks(i.e., each layer is independently formed by the algorithm proposed by Watts and Strogatz for generating small-world networks), ER-ER duplex networks(i.e., each layer is independently generated by the algorithm proposed by Erd ¨os and Renyi) and BA-BA duplex networks(i.e., each layer is independently formed by the classical BA algorithm). Namely,the faster the intra-layer couplings are reconnected, the faster the duplex networks reach global synchronization. Furthermore,we find that by increasing the intra-or inter-coupling strengths, the WS-WS time-varying network’s global synchronizability is enhanced. Take the WS-WS time-varying network as an example, we find that SDR mechanism has greater impact on global synchronizability than MPR mechanism and DPR mechanism. The related dynamical networks can arrive at synchronization faster by SDR than by MPR or DPR. Thus, we only study the effects of SDR on ER-ER duplex networks and BA-BA duplex networks. In addition, we obtain the fact via numerical simulations that, switching intra-layer coupling topologies under SDR mechanism has the greatest impact on the BA-BA duplex network, followed by the ER-ER network, and has the weakest influence on the WS-WS duplex network in terms of improving the global synchronizability when all the intra-layer networks are sparse and have the same average degree. Finally, the global synchronizability of WS-WS and BA-BA time-varying networks is improved compared with static duplex networks, the reason being that the networks tend to be randomized under SDR according to analysis of the networks’ average clustering coefficients and degree distributions.展开更多
基金supported by the National Science and Technology Major Project of China(Grant No.2014ZX10004001-014)the National Natural Science Foundation of China(Grant Nos.61573262,61532020&11472290)the Fundamental Research Funds for the Central Universities(Grant No.2014201020206)
文摘The topological structure of a complex dynamical network plays a vital role in determining the network＇s evolutionary mecha- nisms and functional behaviors, thus recognizing and inferring the network structure is of both theoretical and practical signif- icance. Although various approaches have been proposed to estimate network topologies, many are not well established to the noisy nature of network dynamics and ubiquity of transmission delay among network individuals. This paper focuses on to- pology inference of uncertain complex dynamical networks. An auxiliary network is constructed and an adaptive scheme is proposed to track topological parameters. It is noteworthy that the considered network model is supposed to contain practical stochastic perturbations, and noisy observations are taken as control inputs of the constructed auxiliary network. In particular, the control technique can be further employed to locate hidden sources （or latent variables） in networks. Numerical examples are provided to illustrate the effectiveness of the proposed scheme. In addition, the impact of coupling strength and coupling delay on identification performance is assessed. The proposed scheme provides engineers with a convenient approach to infer topologies of general complex dynamical networks and locate hidden sources, and the detailed performance evaluation can further facilitate practical circuit design.
基金supported by the National Natural Science Foundation of China under Grant Nos.61304022,61573262 and 61573011the Excellent Youth Foundation of Hunan Provincial Department of Education(16B141)
文摘This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchronization criteria for this kind of net works.The results provide an effective way to synchronize discrete-time complex networks by reducing control cost.Furthermore,these theoretical results are illustrated by a complex network via two kinds of pinning schemes.Numerical simulations verify the feasibil计y of the proposed methods.
基金supported by the National Key Research and Development Program of China(Grant No.2018AAA0101100)the National Natural Science Foundation of China(Grant No.61973241)the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)。
文摘Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper.The rewiring mechanisms are named as model-preserving rewiring(MPR), simply direct rewiring(SDR), and degree-preserving rewiring(DPR), respectively. It is found that high switching frequencies will certainly enhance global synchronizability for WSWS duplex networks(i.e., each layer is independently formed by the algorithm proposed by Watts and Strogatz for generating small-world networks), ER-ER duplex networks(i.e., each layer is independently generated by the algorithm proposed by Erd ¨os and Renyi) and BA-BA duplex networks(i.e., each layer is independently formed by the classical BA algorithm). Namely,the faster the intra-layer couplings are reconnected, the faster the duplex networks reach global synchronization. Furthermore,we find that by increasing the intra-or inter-coupling strengths, the WS-WS time-varying network’s global synchronizability is enhanced. Take the WS-WS time-varying network as an example, we find that SDR mechanism has greater impact on global synchronizability than MPR mechanism and DPR mechanism. The related dynamical networks can arrive at synchronization faster by SDR than by MPR or DPR. Thus, we only study the effects of SDR on ER-ER duplex networks and BA-BA duplex networks. In addition, we obtain the fact via numerical simulations that, switching intra-layer coupling topologies under SDR mechanism has the greatest impact on the BA-BA duplex network, followed by the ER-ER network, and has the weakest influence on the WS-WS duplex network in terms of improving the global synchronizability when all the intra-layer networks are sparse and have the same average degree. Finally, the global synchronizability of WS-WS and BA-BA time-varying networks is improved compared with static duplex networks, the reason being that the networks tend to be randomized under SDR according to analysis of the networks’ average clustering coefficients and degree distributions.
