American Institute of Mathematical Sciences

Advanced
March  2015, 10(1): i-iii. doi: 10.3934/nhm.2015.10.1i

Preface: "New trends, models and applications in complex and multiplex networks"

Rosa M. Benito 1, , Regino Criado 2, , Juan C. Losada 1, and  Miguel Romance 2,

1. 

Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, ETSI Agrónomos, 28040, Madrid, Spain, Spain
2. 

Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain, Spain

Published  February 2015

The real world surrounding us is full of complex systems from various types and categories. Internet, the World Wide Web, biological and biochemical networks (brain, metabolic, protein and genomic networks), transport networks (underground, train, airline networks, road networks), communication networks (computer servers, Internet, online social networks), and many others (social community networks, electric power grids and water supply networks,...) are a few examples of the many existing kinds and types of networks [1,2,3,4,6,8,9,10,11]. In the recent past years, the study of structure and dynamics of complex networks has been the subject of intense interest. Recent advances in the study of complex networked systems has put the spotlight on the existence of more than one type of links whose interplay can affect the structure and function of those systems [5,7]. In these networks, relevant information may not be captured if the single layers are analyzed separately, since these different components and units interact with others through different channels of connectivity and dependencies. The global characteristics and behavior of these systems depend on multiple dimensions of integration, relationship or cleavage of its units.

For more information please click the “Full Text” above.
Citation: Rosa M. Benito, Regino Criado, Juan C. Losada, Miguel Romance. Preface: "New trends, models and applications in complex and multiplex networks". Networks & Heterogeneous Media, 2015, 10 (1) : i-iii. doi: 10.3934/nhm.2015.10.1i
References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 10.1103/RevModPhys.74.47.  Google Scholar

[2]

A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.  Google Scholar

[3]

Y. Bar-Yam, Dynamics of Complex Systems, $1^{st}$ Edition, Addison-Wesley, Boston, 1997.  Google Scholar

[4]

A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, $1^{st}$ Edition, Cambridge University Press, New York, 2008. doi: 10.1017/CBO9780511791383.  Google Scholar

[5]

S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001.  Google Scholar

[6]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-308. doi: 10.1016/j.physrep.2005.10.009.  Google Scholar

[7]

M. De Domenico, A. Solè-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. A. Porter, S. Gómez and A. Arenas, Mathematical formulation of multi-layer networks, Phys. Rev. X, 3 (2013), 399-404. Google Scholar

[8]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.  Google Scholar

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The Structure and Dynamics of Networks, Princeton University Press, Princeton, NJ., 2006.  Google Scholar

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. Google Scholar

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. Google Scholar

show all references

References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 10.1103/RevModPhys.74.47.  Google Scholar

[2]

A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.  Google Scholar

[3]

Y. Bar-Yam, Dynamics of Complex Systems, $1^{st}$ Edition, Addison-Wesley, Boston, 1997.  Google Scholar

[4]

A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, $1^{st}$ Edition, Cambridge University Press, New York, 2008. doi: 10.1017/CBO9780511791383.  Google Scholar

[5]

S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001.  Google Scholar

[6]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-308. doi: 10.1016/j.physrep.2005.10.009.  Google Scholar

[7]

M. De Domenico, A. Solè-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. A. Porter, S. Gómez and A. Arenas, Mathematical formulation of multi-layer networks, Phys. Rev. X, 3 (2013), 399-404. Google Scholar

[8]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.  Google Scholar

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The Structure and Dynamics of Networks, Princeton University Press, Princeton, NJ., 2006.  Google Scholar

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. Google Scholar

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. Google Scholar

[1]

Abdon Atangana, Zakia Hammouch, Kolade M. Owolabi, Gisele Mephou. Preface: New trends on numerical analysis and analytical methods with their applications to real world problems. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : i-i. doi: 10.3934/dcdss.201903i
[2]

Abdon Atangana, José Francisco Gómez-Aguilar, Jordan Y. Hristov, Kolade M. Owolabi. Preface on "New trends of numerical and analytical methods". Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : i-ii. doi: 10.3934/dcdss.20203i
[3]

Regino Criado, Rosa M. Benito, Miguel Romance, Juan C. Losada. Preface: Mesoscales and evolution in complex networks: Applications and related topics. Networks & Heterogeneous Media, 2012, 7 (3) : i-iii. doi: 10.3934/nhm.2012.7.3i
[4]

Tomás Caraballo, Juan L. G. Guirao. New trends on nonlinear dynamics and its applications. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : i-ii. doi: 10.3934/dcdss.2015.8.6i
[5]

Manisha Pujari, Rushed Kanawati. Link prediction in multiplex networks. Networks & Heterogeneous Media, 2015, 10 (1) : 17-35. doi: 10.3934/nhm.2015.10.17
[6]

Fathalla A. Rihan, Yang Kuang, Gennady Bocharov. From the guest editors: "Delay Differential Equations: Theory, Applications and New Trends". Discrete & Continuous Dynamical Systems - S, 2020, 13 (9) : i-iv. doi: 10.3934/dcdss.2020404
[7]

Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1295-1317. doi: 10.3934/mbe.2014.11.1295
[8]

Fabio Ancona, Laura Caravenna, Annalisa Cesaroni, Giuseppe M. Coclite, Claudio Marchi, Andrea Marson. Analysis and control on networks: Trends and perspectives. Networks & Heterogeneous Media, 2017, 12 (3) : i-ii. doi: 10.3934/nhm.201703i
[9]

Fabio Ancona, Laura Caravenna, Annalisa Cesaroni, Giuseppe M. Coclite, Claudio Marchi, Andrea Marson. Analysis and control on networks: Trends and perspectives. Networks & Heterogeneous Media, 2017, 12 (2) : i-ii. doi: 10.3934/nhm.201702i
[10]

Suoqin Jin, Fang-Xiang Wu, Xiufen Zou. Domain control of nonlinear networked systems and applications to complex disease networks. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2169-2206. doi: 10.3934/dcdsb.2017091
[11]

Manel Hmimida, Rushed Kanawati. Community detection in multiplex networks: A seed-centric approach. Networks & Heterogeneous Media, 2015, 10 (1) : 71-85. doi: 10.3934/nhm.2015.10.71
[12]

Alain Miranville, Ulisse Stefanelli, Lev Truskinovsky, Augusto Visintin. Preface: Applications of mathematics to mechanics. Discrete & Continuous Dynamical Systems - S, 2017, 10 (1) : i-ii. doi: 10.3934/dcdss.201701i
[13]

Carlos Castillo-Chavez, Baojun Song. Dynamical Models of Tuberculosis and Their Applications. Mathematical Biosciences & Engineering, 2004, 1 (2) : 361-404. doi: 10.3934/mbe.2004.1.361
[14]

Meihong Qiao, Anping Liu, Qing Tang. The dynamics of an HBV epidemic model on complex heterogeneous networks. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1393-1404. doi: 10.3934/dcdsb.2015.20.1393
[15]

Mahendra Piraveenan, Mikhail Prokopenko, Albert Y. Zomaya. On congruity of nodes and assortative information content in complex networks. Networks & Heterogeneous Media, 2012, 7 (3) : 441-461. doi: 10.3934/nhm.2012.7.441
[16]

F. S. Vannucchi, S. Boccaletti. Chaotic spreading of epidemics in complex networks of excitable units. Mathematical Biosciences & Engineering, 2004, 1 (1) : 49-55. doi: 10.3934/mbe.2004.1.49
[17]

Chol-Ung Choe, Thomas Dahms, Philipp Hövel, Eckehard Schöll. Control of synchrony by delay coupling in complex networks. Conference Publications, 2011, 2011 (Special) : 292-301. doi: 10.3934/proc.2011.2011.292
[18]

Xiwei Liu, Tianping Chen, Wenlian Lu. Cluster synchronization for linearly coupled complex networks. Journal of Industrial & Management Optimization, 2011, 7 (1) : 87-101. doi: 10.3934/jimo.2011.7.87
[19]

Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 72-78. doi: 10.3934/proc.1998.1998.72
[20]

Vesselin Petkov, Luchezar Stoyanov. Ruelle transfer operators with two complex parameters and applications. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6413-6451. doi: 10.3934/dcds.2016077

2020 Impact Factor: 1.213

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences