September  2012, 7(3): 385-397. doi: 10.3934/nhm.2012.7.385

Modeling international crisis synchronization in the world trade web

1. 

Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Països Catalans 26, 43007 Tarragona, Spain, Spain, Spain

2. 

Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain

Received  December 2011 Revised  June 2012 Published  October 2012

Trade is a fundamental pillar of economy and a form of social organization. Its empirical characterization at the worldwide scale is represented by the World Trade Web (WTW), the network built upon the trade relationships between the different countries. Several scientific studies have focused on the structural characterization of this network, as well as its dynamical properties, since we have registry of the structure of the network at different times in history. In this paper we study an abstract scenario for the development of global crises on top of the structure of connections of the WTW. Assuming a cyclic dynamics of national economies and the interaction of different countries according to the import-export balances, we are able to investigate, using a simple model of pulse-coupled oscillators, the synchronization phenomenon of crises at the worldwide scale. We focus on the level of synchronization measured by an order parameter at two different scales, one for the global system and another one for the mesoscales defined through the topology. We use the WTW network structure to simulate a network of Integrate-and-Fire oscillators for six different snapshots between years 1950 and 2000. The results reinforce the idea that globalization accelerates the global synchronization process, and the analysis at a mesoscopic level shows that this synchronization is different before and after globalization periods: after globalization, the effect of communities is almost inexistent.
Citation: Pau Erola, Albert Díaz-Guilera, Sergio Gómez, Alex Arenas. Modeling international crisis synchronization in the world trade web. Networks & Heterogeneous Media, 2012, 7 (3) : 385-397. doi: 10.3934/nhm.2012.7.385
References:
[1]

A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno and C. Zhou, Synchronization in complex networks,, Phys. Rep., 469 (2008), 93.  doi: 10.1016/j.physrep.2008.09.002.  Google Scholar

[2]

A. Arenas, J. Duch, A. Fernández and S. Gómez, Size reduction of complex networks preserving modularity,, New J. Phys., 9 (2007), 1.   Google Scholar

[3]

A. Arenas, A. Fernández and S. Gómez, Analysis of the structure of complex networks at different resolution levels,, New J. Phys., 10 (2008).  doi: 10.1088/1367-2630/10/5/053039.  Google Scholar

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U. Brandes, D. Delling, M. Gaertler, R. Goerke, M. Hoefer, Z. Nikoloski and D. Wagner, On modularity clustering,, IEEE T. Knowl. Data En., 20 (2008), 172.  doi: 10.1109/TKDE.2007.190689.  Google Scholar

[6]

S. R. Campbell, D. L. L. Wang and C. Jayaprakash, Synchrony and desynchrony in integrate-and-fire oscillators,, Neural Comput., 11 (1999), 1595.  doi: 10.1162/089976699300016160.  Google Scholar

[7]

A. Clauset, M. E. J. Newman and C. Moore, Finding community structure in very large networks,, Phys. Rev. E, 70 (2004).  doi: 10.1103/PhysRevE.70.066111.  Google Scholar

[8]

A. V. Deardorff, "Terms of Trade: Glossary of International Economics,'', World Scientific, (2006).   Google Scholar

[9]

J. Duch and A. Arenas, Community identification using extremal optimization,, Phys. Rev. E, 72 (2005).  doi: 10.1103/PhysRevE.72.027104.  Google Scholar

[10]

G. Fagiolo, J. Reyes and S. Schiavo, World-trade web: Topological properties, dynamics, and evolution,, Phys. Rev. E, 79 (2009).  doi: 10.1103/PhysRevE.79.036115.  Google Scholar

[11]

D. Garlaschelli, T. Di Matteo, T. Aste, G. Caldarelli and M. I. Loffredo, Interplay between topology and dynamics in the World Trade Web,, Eur. Phys. J. B, 57 (2007), 159.  doi: 10.1140/epjb/e2007-00131-6.  Google Scholar

[12]

R. Guimerà and L. A. N. Amaral, Cartography of complex networks: modules and universal roles,, J. Stat. Mech., (2005).   Google Scholar

[13]

K. S. Gleditsch, Expanded Trade and GDP data,, J. Conflict Resolut., 46 (2002), 712.  doi: 10.1177/002200202236171.  Google Scholar

[14]

J. He and M. W. Deem, Structure and response in the World Trade Network,, Phys. Rev. Lett., 105 (2010).  doi: 10.1103/PhysRevLett.105.198701.  Google Scholar

[15]

M. A. Kose, C. Otrok and E. S. Prasad, Global business cycles: Convergence or decoupling?,, Nat. Bureau of Economic Research, 14292 (2008).   Google Scholar

[16]

H. P. Minsky, "Stabilizing an Unstable Economy,'', Yale University Press, (1986).   Google Scholar

[17]

H. P. Minsky, The financial instability hypothesis,, The Jerome Levy Economics Institute, 74 (1992).   Google Scholar

[18]

R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators,, SIAM J. Appl. Math., 50 (1990), 1645.  doi: 10.1137/0150098.  Google Scholar

[19]

M. E. J. Newman, Analysis of weighted networks,, Phys. Rev. E, 70 (2004).  doi: 10.1103/PhysRevE.70.056131.  Google Scholar

[20]

M. E. J. Newman, Fast algorithm for detecting community structure in networks,, Phys. Rev. E, 69 (2004).  doi: 10.1103/PhysRevE.69.066133.  Google Scholar

[21]

M. E. J. Newman, Modularity and community structure in networks,, P. Natl. Acad. Sci. USA, 103 (2006), 8577.  doi: 10.1073/pnas.0601602103.  Google Scholar

[22]

X. Li, Y. Y. Jin and G. Chen, Complexity and synchronization of the world trade web,, Physica A, 328 (2003), 287.  doi: 10.1016/S0378-4371(03)00567-3.  Google Scholar

[23]

J. M. Pujol, J. Béjar and J. Delgado, Clustering algorithm for determining community structure in large networks,, Phys. Rev. E, 74 (2006).  doi: 10.1103/PhysRevE.74.016107.  Google Scholar

[24]

A. Rothkegel and K. Lehnertz, Recurrent events of synchrony in complex networks of pulse-coupled oscillators,, Europhys. Lett., 95 (2011).  doi: 10.1209/0295-5075/95/38001.  Google Scholar

[25]

M. A. Serrano and M. Boguñá, Topology of the world trade web,, Phys. Rev. E, 68 (2003).  doi: 10.1103/PhysRevE.68.015101.  Google Scholar

[26]

T. Squartini, G. Fagiolo and D. Garlaschelli, Randomizing world trade. I. A binary network analysis,, Phys. Rev. E, 84 (2011).  doi: 10.1103/PhysRevE.84.046118.  Google Scholar

[27]

M. Timme, F. Wolf and T. Geisel, Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators,, Phys. Rev. Lett, 89 (2002).  doi: 10.1103/PhysRevLett.89.258701.  Google Scholar

show all references

References:
[1]

A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno and C. Zhou, Synchronization in complex networks,, Phys. Rep., 469 (2008), 93.  doi: 10.1016/j.physrep.2008.09.002.  Google Scholar

[2]

A. Arenas, J. Duch, A. Fernández and S. Gómez, Size reduction of complex networks preserving modularity,, New J. Phys., 9 (2007), 1.   Google Scholar

[3]

A. Arenas, A. Fernández and S. Gómez, Analysis of the structure of complex networks at different resolution levels,, New J. Phys., 10 (2008).  doi: 10.1088/1367-2630/10/5/053039.  Google Scholar

[4]

E. T. Bell, Exponential numbers,, Am. Math. Mon., 41 (1934), 411.  doi: 10.2307/2300300.  Google Scholar

[5]

U. Brandes, D. Delling, M. Gaertler, R. Goerke, M. Hoefer, Z. Nikoloski and D. Wagner, On modularity clustering,, IEEE T. Knowl. Data En., 20 (2008), 172.  doi: 10.1109/TKDE.2007.190689.  Google Scholar

[6]

S. R. Campbell, D. L. L. Wang and C. Jayaprakash, Synchrony and desynchrony in integrate-and-fire oscillators,, Neural Comput., 11 (1999), 1595.  doi: 10.1162/089976699300016160.  Google Scholar

[7]

A. Clauset, M. E. J. Newman and C. Moore, Finding community structure in very large networks,, Phys. Rev. E, 70 (2004).  doi: 10.1103/PhysRevE.70.066111.  Google Scholar

[8]

A. V. Deardorff, "Terms of Trade: Glossary of International Economics,'', World Scientific, (2006).   Google Scholar

[9]

J. Duch and A. Arenas, Community identification using extremal optimization,, Phys. Rev. E, 72 (2005).  doi: 10.1103/PhysRevE.72.027104.  Google Scholar

[10]

G. Fagiolo, J. Reyes and S. Schiavo, World-trade web: Topological properties, dynamics, and evolution,, Phys. Rev. E, 79 (2009).  doi: 10.1103/PhysRevE.79.036115.  Google Scholar

[11]

D. Garlaschelli, T. Di Matteo, T. Aste, G. Caldarelli and M. I. Loffredo, Interplay between topology and dynamics in the World Trade Web,, Eur. Phys. J. B, 57 (2007), 159.  doi: 10.1140/epjb/e2007-00131-6.  Google Scholar

[12]

R. Guimerà and L. A. N. Amaral, Cartography of complex networks: modules and universal roles,, J. Stat. Mech., (2005).   Google Scholar

[13]

K. S. Gleditsch, Expanded Trade and GDP data,, J. Conflict Resolut., 46 (2002), 712.  doi: 10.1177/002200202236171.  Google Scholar

[14]

J. He and M. W. Deem, Structure and response in the World Trade Network,, Phys. Rev. Lett., 105 (2010).  doi: 10.1103/PhysRevLett.105.198701.  Google Scholar

[15]

M. A. Kose, C. Otrok and E. S. Prasad, Global business cycles: Convergence or decoupling?,, Nat. Bureau of Economic Research, 14292 (2008).   Google Scholar

[16]

H. P. Minsky, "Stabilizing an Unstable Economy,'', Yale University Press, (1986).   Google Scholar

[17]

H. P. Minsky, The financial instability hypothesis,, The Jerome Levy Economics Institute, 74 (1992).   Google Scholar

[18]

R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators,, SIAM J. Appl. Math., 50 (1990), 1645.  doi: 10.1137/0150098.  Google Scholar

[19]

M. E. J. Newman, Analysis of weighted networks,, Phys. Rev. E, 70 (2004).  doi: 10.1103/PhysRevE.70.056131.  Google Scholar

[20]

M. E. J. Newman, Fast algorithm for detecting community structure in networks,, Phys. Rev. E, 69 (2004).  doi: 10.1103/PhysRevE.69.066133.  Google Scholar

[21]

M. E. J. Newman, Modularity and community structure in networks,, P. Natl. Acad. Sci. USA, 103 (2006), 8577.  doi: 10.1073/pnas.0601602103.  Google Scholar

[22]

X. Li, Y. Y. Jin and G. Chen, Complexity and synchronization of the world trade web,, Physica A, 328 (2003), 287.  doi: 10.1016/S0378-4371(03)00567-3.  Google Scholar

[23]

J. M. Pujol, J. Béjar and J. Delgado, Clustering algorithm for determining community structure in large networks,, Phys. Rev. E, 74 (2006).  doi: 10.1103/PhysRevE.74.016107.  Google Scholar

[24]

A. Rothkegel and K. Lehnertz, Recurrent events of synchrony in complex networks of pulse-coupled oscillators,, Europhys. Lett., 95 (2011).  doi: 10.1209/0295-5075/95/38001.  Google Scholar

[25]

M. A. Serrano and M. Boguñá, Topology of the world trade web,, Phys. Rev. E, 68 (2003).  doi: 10.1103/PhysRevE.68.015101.  Google Scholar

[26]

T. Squartini, G. Fagiolo and D. Garlaschelli, Randomizing world trade. I. A binary network analysis,, Phys. Rev. E, 84 (2011).  doi: 10.1103/PhysRevE.84.046118.  Google Scholar

[27]

M. Timme, F. Wolf and T. Geisel, Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators,, Phys. Rev. Lett, 89 (2002).  doi: 10.1103/PhysRevLett.89.258701.  Google Scholar

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