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Brede M, Stella M, Kalloniatis AC. Competitive influence maximization and enhancement of synchronization in populations of non-identical Kuramoto oscillators. Sci Rep 2018; 8:702. [PMID: 29335434 PMCID: PMC5768883 DOI: 10.1038/s41598-017-18961-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Accepted: 12/15/2017] [Indexed: 11/10/2022] Open
Abstract
Many networked systems have evolved to optimize performance of function. Much literature has considered optimization of networks by central planning, but investigations of network formation amongst agents connecting to achieve non-aligned goals are comparatively rare. Here we consider the dynamics of synchronization in populations of coupled non-identical oscillators and analyze adaptations in which individual nodes attempt to rewire network topology to optimize node-specific aims. We demonstrate that, even though individual nodes’ goals differ very widely, rewiring rules in which each node attempts to connect to the rest of the network in such a way as to maximize its influence on the system can enhance synchronization of the collective. The observed speed-up of consensus finding in this competitive dynamics might explain enhanced synchronization in real world systems and shed light on mechanisms for improved consensus finding in society.
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Affiliation(s)
- Markus Brede
- University of Southampton, Electronics and Computer Science, Southampton, SO171BJ, UK.
| | - Massimo Stella
- University of Southampton, Electronics and Computer Science, Southampton, SO171BJ, UK.,Fondazione Bruno Kessler, Trento, Italy
| | - Alexander C Kalloniatis
- Joint and Operations Analysis Division, Defence Science and Technology Group, Canberra, 2600, Australia
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Guo Q, Liang G, Fu JQ, Han JT, Liu JG. Roles of mixing patterns in the network reconstruction. Phys Rev E 2016; 94:052303. [PMID: 27967098 DOI: 10.1103/physreve.94.052303] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Indexed: 11/07/2022]
Abstract
Compressive sensing is an effective way to reconstruct the network structure. In this paper, we investigate the effect of the mixing patterns, measured by the assortative coefficient, on the performance of network reconstruction. First, we present a model to generate networks with different assortativity coefficients, then we reconstruct the network structure by using the compressive sensing method. The experimental results show that when the assortativity coefficient r=0.2, the accuracy of the network reconstruction reaches the maximum value, which suggests that the compressive sensing is more effective for uncovering the links of social networks. Moreover, the accuracy of the network reconstruction will be higher as the network size increases.
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Affiliation(s)
- Qiang Guo
- Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China
| | - Guang Liang
- Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China
| | - Jia-Qi Fu
- Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China
| | - Jing-Ti Han
- Data Science and Cloud Service Research Centre, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China
| | - Jian-Guo Liu
- Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China.,Data Science and Cloud Service Research Centre, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China
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Qu J, Wang SJ, Jusup M, Wang Z. Effects of random rewiring on the degree correlation of scale-free networks. Sci Rep 2015; 5:15450. [PMID: 26482005 PMCID: PMC4611853 DOI: 10.1038/srep15450] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Accepted: 09/08/2015] [Indexed: 01/01/2023] Open
Abstract
Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature. We comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same. Consequently, the network dynamics is changed, which is proven here by means of the biased random walk.
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Affiliation(s)
- Jing Qu
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
| | - Sheng-Jun Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
| | - Marko Jusup
- Faculty of Sciences, Kyushu University, Fukuoka 819-0395, Japan
| | - Zhen Wang
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
- School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
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Peron TKD, Ji P, Rodrigues FA, Kurths J. Effects of assortative mixing in the second-order Kuramoto model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052805. [PMID: 26066210 DOI: 10.1103/physreve.91.052805] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Indexed: 06/04/2023]
Abstract
In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.
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Affiliation(s)
- Thomas K Dm Peron
- Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, São Paulo, Brazil
| | - Peng Ji
- Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany
- Department of Physics, Humboldt University, 12489 Berlin, Germany
| | - Francisco A Rodrigues
- Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany
- Department of Physics, Humboldt University, 12489 Berlin, Germany
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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Sendiña-Nadal I, Leyva I, Navas A, Villacorta-Atienza JA, Almendral JA, Wang Z, Boccaletti S. Effects of degree correlations on the explosive synchronization of scale-free networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032811. [PMID: 25871161 DOI: 10.1103/physreve.91.032811] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2014] [Indexed: 06/04/2023]
Abstract
We study the organization of finite-size, large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are known to occur in growing scale-free networks, while the transition has a completely different nature for static random configurations preserving the same structure-dynamics correlation. We show that the further presence of degree-degree correlations in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in scale-free networks. The latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.
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Affiliation(s)
- I Sendiña-Nadal
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - I Leyva
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - A Navas
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - J A Villacorta-Atienza
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - J A Almendral
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - Z Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
- Center for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong) and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
| | - S Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy
- Italian Embassy in Israel, 25 Hamered Street, 68125 Tel Aviv, Israel
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Zhu L, Tian L, Shi D. Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042921. [PMID: 24229263 DOI: 10.1103/physreve.88.042921] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Indexed: 06/02/2023]
Abstract
The emergence of explosive synchronization transitions in networks of phase oscillators recently has become one of the most interesting topics. It is widely believed that the large frequency mismatch of a pair of oscillators (also known as disassortativity in frequency) is a direct cause of an explosive synchronization. It is found that, besides the disassortativity in frequency, the disassortativity in node degree also shows up in connection with the first-order synchronization transition. In this paper, we simulate the Kuramoto model on top of a family of networks with different degree-degree and frequency-frequency correlation patterns. Results show that only when the degrees and natural frequencies of the network's nodes are both disassortative can an explosive synchronization occur.
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Affiliation(s)
- Liuhua Zhu
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
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Chen H, He G, Huang F, Shen C, Hou Z. Explosive synchronization transitions in complex neural networks. CHAOS (WOODBURY, N.Y.) 2013; 23:033124. [PMID: 24089960 DOI: 10.1063/1.4818543] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.
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Affiliation(s)
- Hanshuang Chen
- School of Physics and Materials Science, Anhui University, Hefei 230039, People's Republic of China
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Chen H, Hou Z, Xin H, Yan Y. Statistically consistent coarse-grained simulations for critical phenomena in complex networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011107. [PMID: 20866565 DOI: 10.1103/physreve.82.011107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2010] [Revised: 05/17/2010] [Indexed: 05/29/2023]
Abstract
We propose a degree-based coarse-graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium dynamical flows. For the Ising model and susceptible-infected-susceptible epidemic model, we introduce these required conditions explicitly and further prove that they are satisfied by our coarse-grained network construction within the annealed network approximation. Finally, we numerically show that the phase transitions and fluctuations on the coarse-grained network are all in good agreements with those on the original one.
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Affiliation(s)
- Hanshuang Chen
- Department of Chemical Physics, Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
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Zhang Z, Zhang Y, Zhou S, Yin M, Guan J. Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks. JOURNAL OF MATHEMATICAL PHYSICS 2009; 50:033514. [PMID: 32255840 PMCID: PMC7110918 DOI: 10.1063/1.3094757] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2008] [Accepted: 02/12/2009] [Indexed: 05/28/2023]
Abstract
Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution P ( k ) ∼ k - γ , where the degree exponent γ describes the extent of heterogeneity. In this paper, we study analytically the average path length (APL) of and random walks (RWs) on a family of deterministic networks, recursive scale-free trees (RSFTs), with negative degree correlations and various γ ∊ ( 2 , 1 + ln 3 / ln 2 ] , with an aim to explore the impacts of structure heterogeneity on the APL and RWs. We show that the degree exponent γ has no effect on the APL d of RSFTs: In the full range of γ , d behaves as a logarithmic scaling with the number of network nodes N (i.e., d ∼ ln N ), which is in sharp contrast to the well-known double logarithmic scaling ( d ∼ ln ln N ) previously obtained for uncorrelated scale-free networks with 2 ≤ γ < 3 . In addition, we present that some scaling efficiency exponents of random walks are reliant on the degree exponent γ .
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Affiliation(s)
| | - Yichao Zhang
- Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, China
| | | | | | - Jihong Guan
- Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, China
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Baptista MS, de Carvalho JX, Hussein MS. Finding quasi-optimal network topologies for information transmission in active networks. PLoS One 2008; 3:e3479. [PMID: 18941516 PMCID: PMC2565798 DOI: 10.1371/journal.pone.0003479] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2008] [Accepted: 09/30/2008] [Indexed: 11/18/2022] Open
Abstract
This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.
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Affiliation(s)
- Murilo S Baptista
- Max-Planck-Institut für Physik komplexer Systeme, Dresden, Deutschland.
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13
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Rong Z, Li X, Wang X. Roles of mixing patterns in cooperation on a scale-free networked game. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:027101. [PMID: 17930177 DOI: 10.1103/physreve.76.027101] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2007] [Indexed: 05/25/2023]
Abstract
We investigate how the degree-mixing pattern affects the emergence of cooperation in the networked prisoner's dilemma game. Our study shows that when a network becomes assortative mixing by degree, the large-degree vertices (hubs) tend to interconnect to each other closely, which destroys the sustainability among cooperators and promotes the invasion of defectors, whereas in disassortative networks, the isolation among hubs protects the cooperative hubs in holding onto their initial strategies to avoid extinction.
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Affiliation(s)
- Zhihai Rong
- Complex Networks and Control Lab, Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
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