This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability met...This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability method,we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions,and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers.Interestingly,for a certain class of coupling matrices across layers,it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger,intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers.Finally,numerical simulations further verify the theoretical results.展开更多
This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions hav...This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.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Project supported in part by the National Natural Science Foundation of China(Grant Nos.61573004 and 11501221)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-YX301)+1 种基金the Program for New Century Excellent Talents in Fujian Province University in 2016the Project of Education and Scientific Research for Middle and Young Teachers in Fujian Province,China(Grant Nos.JAT170027 and JA15030)
文摘This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability method,we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions,and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers.Interestingly,for a certain class of coupling matrices across layers,it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger,intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers.Finally,numerical simulations further verify the theoretical results.
基金supported by the National Key Research and Development Program of China (Grant No. 2016YFB0800401)the National Natural Science Foundation of China (Grant Nos. 61621003, 61532020, 61573262, 61573004)+3 种基金the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQNYX301, ZQN-PY401)the Natural Science Foundation of Fujian Province (Grant Nos. 2015J01260, 2015J01584)the Program for New Century Excellent Talents in Fujian Province University in 2016the Cultivation Program for Outstanding Young Scientific Talents of the Higher Education Institutions of Fujian Province in 2016
文摘This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.
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.
