Summary
Previous chapters have discussed tools from graph theory and their contribution to our understanding of the structural organization of mammalian brains and its functional implications. The brain functions are mediated by complicated dynamical processes which arise from the underlying complex neural networks, and synchronization has been proposed as an important mechanism for neural information processing. In this chapter, we discuss synchronization dynamics on complex networks. We first present a general theory and tools to characterize the relationship of some structural measures of networks to their synchronizability (the ability of the networks to achieve complete synchronization) and to the organization of effective synchronization patterns on the networks. Then, we study synchronization in a realistic network of cat cortical connectivity by modeling the nodes (which are cortical areas composed of large ensembles of neurons) by a neural mass model or a subnetwork of interacting neurons. We show that if the dynamics is characterized by well-defined oscillations (neural mass model and subnetworks with strong couplings), the synchronization patterns can be understood by the general principles discussed in the first part of the chapter. With weak couplings, the model with subnetworks displays biologically plausible dynamics and the synchronization pattern reveals a hierarchically clustered organization in the network structure. Thus, the study of synchronization of complex networks can provide insights into the relationship between network topology and functional organization of complex brain networks.
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References
See, e.g., reviews: S. H. Strogatz, Nature (London) 410, 268 (2001); R. Albert and A.-L. Barab’asi, Rev. Mod. Phys. 74, 47 (2002); S. Boccaletti et al., Phys. Rep. 424, 175 (2006).
D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).
A.-L. Barabàsi and R. Albert, Science 286, 509 (1999).
R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chlkovskii and U. Alon, Science 298, 824 (2002).
A partial list, e.g., P. M. Gade and C. K. Hu, Phys. Rev. E 62, 6409 (2000); J. Jost and M. P. Joy, Phys. Rev. E 65, 016201 (2001); M. Barahona and L. M. Pecora, Phys. Rev. Lett. 89, 054101 (2002); A. E. Motter, C. S.Zhou and J. Kurths, Europhys. Lett. 69, 334 (2005); Phys. Rev. E 71, 016116 (2005); L. Donetti, P. I. Hurtado and M. A. Munoz, Phys. Rev. Lett. 95, 188701 (2005); A. Arenas, A. Di’az-Guilera and C. J. Per’ez-Vicentz, Phys. Rev. Lett. 96, 114102 (2006).
E. Salinas and T. J. Sejnowski, Nature Neurosci. 2, 539 (2001); P. Fri’es, Trends Cogn. Sci. 9, 474 (2005); A. Schnitzler and J. Gross, Nature Neurosci. 6, 285 (2005).
L. F. Lago-Fern’andez, R. Huerta, F. Corbacho and J. A. Sigüenza, Phys. Rev. Lett. 84, 2758 (2000).
N. Masuda and K. Aihara, Biol. Cybern. 90, 302 (2004).
X. Guardiola, A. Diaz-Guilera, M. Llas and C. J. Per’ez, Phys. Rev. E 62, 5565 (2000).
M. Timme, F. Wolf and yT. Geisel, Phys. Rev. Lett. 92, 074101 (2004); M. Denker, M. Timme, M. Diesmann, F. Wolf and T. Geisel, Phys. Rev. Lett. 92, 074103 (2004); V. N Belykh, E. de Lange and M. Hasler, Phys. Rev. Lett. 94, 188101 (2005).
H. Hong, M. Y. Choi and B. J. Kim, Phys. Rev. E 65, 026139 (2002).
A. M. Batista, S. E. D. Pinto, R. L. Viana and S. R. Lopes, Physica A 322, 118 (2003).
T. Nishikawa, A. E. Motter, Y.-C. Lai and F. C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003).
F. Chung and L. Lu, Proc. Natl. Acad. Sci. U.S.A. 99, 15879 (2002); R. Cohen and S. Havlin, Phys. Rev. Lett. 90, 058701 (2003).
J. W. Scannell, G. A. P. C. Burns, C. C. Hilgetag, M. A. O’eil and M. P. Yong, Cereb. Cortex 9, 277 (1999).
B. T. Grenfell, O. N. Bjornstad and J. Kappey, Nature (London) 414, 716 (2001).
G. Korniss, M. A. Novotny, H. Guclu, Z. Toroczkai and P. A. Rikvold, Science 299, 677 (2003).
A. Barrat, M. Barth’elemy, R. Pastor-Satorras and A. Vespignani, Proc. Natl. Acad. Sci. U.S.A. 101, 3747 (2004).
A. E. Motter, C. S. Zhou and J. Kurths, Europhys. Lett. 69, 334 (2005); Phys. Rev. E 71, 016116 (2005).
M. Chavez, D.-U. Hwang, A. Amann, H. G. E. Hentschel and S. Boccaletti, Phys. Rev. Lett. 94, 218701 (2005).
C. S. Zhou, A.E. Motter and J. Kurths, Phys. Rev. Lett. 96, 034101 (2006).
C. S. Zhou and J. Kurths, Phys. Rev. Lett. 96, 164102 (2006).
L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
L. M. Pecora and M. Barahona, Chaos and Complexity Lett. 1, 61 (2005).
F. Chung, L. Lu and V. Vu, Proc. Natl. Acad. Sci. U.S.A. 100, 6313 (2003).
X. F. Wang, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 885 (2002).
J. Jost and M. P. Joy, Phys. Rev. E 65, 016201 (2001).
S. Jalan and R. E. Amritkar, Phys. Rev. Lett. 90, 014101 (2003).
S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E 62, 1842 (2000).
M. E. J. Newman, S. H. Strogatz and D. J. Watts, Phys. Rev. E 64, 026118 (2001).
C. S. Zhou and J. Kurths, Chaos 16, 015104 (2006).
M. Rosenblum, A. Pikovsky and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
A. S. Pikovsky, M. Rosenblum and J. Kurths, Synchronization – A universal concept in nonlinear sciences, Cambridge University Press, 2001; S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares and C.S. Zhou, The Synchronization of Chaotic Systems, Phys. Rep. 366, 1–101 (2002).
M. E. J. Newman, C. Moore and D. J. Watts, Phys. Rev. Lett. 84, 3201 (2000).
G. V. Osipov, J. Kurths and C. S. Zhou, Synchronization in Oscillatory Networks, Spring, Berlin, 2007.
C. J. Stam and E. A. de Bruin, Hum. Brain Mapp. 22, 97 (2004).
See a recent review: O. Sporns, D. R. Chialvo, M. Kaiser and C. C. Hilgetag, Trends Cogn. Sci. 8, 418 (2004).
C. J. Stam, Neurosci. Lett. 355, 25 (2004); V. M. Egu’iluz, D. R. Chialvo, G. Cecchi, M. Baliki, and A. V. Apkarian, Phys. Rev. Lett. 94, 018102 (2005); R. Salvador et al., Cereb. Cortex 15, 1332 (2005).
O. Sporns and J. D. Zwi, Neuroinformatics 2, 145 (2004).
C. C. Hilgetag and M. Kaiser, Neuroinformatics 2, 353 (2004).
C. C. Hilgetag, G. A. Burns, M. A. O’Neill, J. W. Scannell and M. P. Young, Phil. Trans. R. Soc. Lond. B. 355, 91 (2000).
M. E. J. Newman and M. Girvan, Phys. Rev. E. 69, 026113 (2004).
F. H. Lopes da Silva, A. Hoeks, H. Smits and L. H. Zetterberg, Kybernetik 15, 27 (1974).
F. Wendling, J. J. Bellanger, F. Bartolomei and P. Chauvel, Biol. Cybern. 83, 367 (2000).
C. S. Zhou, L. Zemanov’a, G. Zamora, C. C. Hilgetag and J. Kurths, Phys. Rev. Lett. 97, 238103 (2006).
L. Zemanov’a, C. S. Zhou, J. Kurths, Physica D 224, 202 (2006).
G. Buzsaki, C. Geisler, D. A. Henze and X. J. Wang, Trends Neurosci. 27, 186 (2004).
M. P. Young, Spat. Vis. 13, 137 (2000).
R. FitzHugh, Biophys. J. 1, 445 (1961).
E. Niedermeyer and F. Lopes da Silva, Electroencephalography: Basic principles, clinical applications, and related fields, Williams & Wilkins, 1993; R. Kandel, J. H., Schwartz, and T. M. Jessell, Principles of Neural Science, McGraw-Hill, 2000.
P. Kudela, P. J. Franaszczuk and G. K. Bergey, Biol. Cybern. 88, 276 (2003).
A. Morrison, C. Mehring, T. Geisel, A. Aertsen and M. Diesmann, Neural Comput. 17, 1776 (2005).
R. Kütter and F. T. Sommer, Phil. Trans. R. Soc. Lond. B 355, 127 (2000).
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Zhou, C., Zemanová, L., Kurths, J. (2007). Synchronization Dynamics in Complex Networks. In: Graben, P.b., Zhou, C., Thiel, M., Kurths, J. (eds) Lectures in Supercomputational Neurosciences. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73159-7_5
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