September  2012, 7(3): i-iii. doi: 10.3934/nhm.2012.7.3i

Preface: Mesoscales and evolution in complex networks: Applications and related topics

1. 

Departamento de Matemática Aplicada, Universidad Rey Juan Carlos (URJC), C/ Tulipán s/n, 28933-Móstoles, Madrid, Spain, Spain

2. 

Departamento de Física y Mecánica, ETSI Agrónomos, Universidad Politécnica de Madrid, C/ Ciudad universitaria s/n, 28040 Madrid, Spain, Spain

Published  October 2012

The study of networks has become one of the paradigms of the science of complexity as well as a fascinating branch of research in applied mathematics, physics, engineering, sociology, biology and science in general. Different systems such as transport networks (underground, train, airline networks, road networks), communication networks (computer servers, Internet, online social networks), neural networks (neural interaction networks and brain networks), biochemical networks (metabolic, protein and genomic networks), trophic networks, social community networks, marketing and recommendation networks, other infrastructure networks (electric power grids, water supply networks) and many others (including the World Wide Web)([1],[3],[4],[7],[8],[9],[10]) are known to have behavioral and structural characteristics in common, and they can be studied by using non-linear mathematical techniques and computer modeling approaches. The interest on complex networks has certainly been promoted by the optimized rating of computing facilities, and by the availability of data on large real networks (including the World Wide Web, cortical networks, citation networks from Scientific Citation Index and online social networks). This focused section is characterized for emphasizing the latest applications of complex networks rather than the theoretical aspects, but covering several aspects as topological properties, algorithms and computation tools, models of interactions between complex systems, synchronization, control and some other related topics.

For more information please click the “Full Text” above.”
Citation: Regino Criado, Rosa M. Benito, Miguel Romance, Juan C. Losada. Preface: Mesoscales and evolution in complex networks: Applications and related topics. Networks and Heterogeneous Media, 2012, 7 (3) : i-iii. doi: 10.3934/nhm.2012.7.3i
References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 0.1103/RevModPhys.74.47.

[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.

[3]

Y. Bar-Yam, "Dynamics of Complex Systems," Addison-Wesley, 1997.

[4]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-303. doi: 10.1016/j.physrep.2005.10.009.

[5]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Resilience of the Internet to random breakdowns, Physical Review Letters, 85 (2000), 4626-4628. doi: 10.1103/PhysRevLett.85.4626.

[6]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Breakdown of the Internet under intentional attacks, Physical Review Letters, 86 (2001), 3682-3685. doi: 10.1103/PhysRevLett.86.3682.

[7]

L. Fontoura Costa, et al, "Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications,'' arXiv:0711.3199v3, [physics.soc-ph], 2006.

[8]

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

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The structure and dynamics of networks, Princeton University Press, Princeton, NJ., 167-256, 2006.

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. doi: 10.1038/35065725.

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

show all references

References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 0.1103/RevModPhys.74.47.

[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.

[3]

Y. Bar-Yam, "Dynamics of Complex Systems," Addison-Wesley, 1997.

[4]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-303. doi: 10.1016/j.physrep.2005.10.009.

[5]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Resilience of the Internet to random breakdowns, Physical Review Letters, 85 (2000), 4626-4628. doi: 10.1103/PhysRevLett.85.4626.

[6]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Breakdown of the Internet under intentional attacks, Physical Review Letters, 86 (2001), 3682-3685. doi: 10.1103/PhysRevLett.86.3682.

[7]

L. Fontoura Costa, et al, "Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications,'' arXiv:0711.3199v3, [physics.soc-ph], 2006.

[8]

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

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The structure and dynamics of networks, Princeton University Press, Princeton, NJ., 167-256, 2006.

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. doi: 10.1038/35065725.

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

[1]

Rosa M. Benito, Regino Criado, Juan C. Losada, Miguel Romance. Preface: "New trends, models and applications in complex and multiplex networks". Networks and Heterogeneous Media, 2015, 10 (1) : i-iii. doi: 10.3934/nhm.2015.10.1i

[2]

Jinhae Park. Preface: Special issue on mathematical study on liquid crystals and related topics: Statics and dynamics. Discrete and Continuous Dynamical Systems - S, 2015, 8 (2) : i-i. doi: 10.3934/dcdss.2015.8.2i

[3]

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

[4]

Michal Beneš, Tetsuya Ishiwata, Takashi Sakamoto, Shigetoshi Yazaki. Preface: Special Issue on recent topics in industrial and applied mathematics. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : i-i. doi: 10.3934/dcdss.2015.8.5i

[5]

Mustapha Mokhtar-Kharroubi. Spectra of structured diffusive population equations with generalized Wentzell-Robin boundary conditions and related topics. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3551-3563. doi: 10.3934/dcdss.2020244

[6]

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

[7]

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

[8]

Toyohiko Aiki, Joost Hulshof, Nobuyuki Kenmochi, Adrian Muntean. Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : i-iii. doi: 10.3934/dcdss.2014.7.1i

[9]

Alessandra Pluda. Evolution of spoon-shaped networks. Networks and Heterogeneous Media, 2016, 11 (3) : 509-526. doi: 10.3934/nhm.2016007

[10]

Nikolay Dimitrov. An example of rapid evolution of complex limit cycles. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 709-735. doi: 10.3934/dcds.2011.31.709

[11]

Wei Xi Li, Chao Jiang Xu. Subellipticity of some complex vector fields related to the Witten Laplacian. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2709-2724. doi: 10.3934/cpaa.2021047

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

Laura Caravenna, Annalisa Cesaroni, Hung Vinh Tran. Preface: Recent developments related to conservation laws and Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (5) : i-iii. doi: 10.3934/dcdss.201805i

[20]

Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Miguel E. Vázquez-Méndez. Optimal control of urban air pollution related to traffic flow in road networks. Mathematical Control and Related Fields, 2018, 8 (1) : 177-193. doi: 10.3934/mcrf.2018008

2020 Impact Factor: 1.213

Metrics

  • PDF downloads (46)
  • HTML views (0)
  • Cited by (0)

[Back to Top]