Cluster synchronization in coupled systems with hub structure

Physica D: Nonlinear Phenomena

Volumn 241, Issue 21, 2012, Pages 1804-1810

  Kitajima, Hiroyuki ^a   Yoshihara, Takakazu ^a  

^a KAGAWA UNIVERSITY   (Japan)

Author keywords

Bifurcation; Complex network; Hub; Synchronization

Indexed keywords

BIFURCATION (MATHEMATICS); COMPLEX NETWORKS;

CENTRAL NODES; CLUSTER SYNCHRONIZATION; COUPLED ELEMENT; COUPLED SYSTEMS; FIRING FREQUENCY; MORRIS-LECAR NEURONS; NEURON MODEL; OSCILLATION FREQUENCY;

SYNCHRONIZATION;

EID: 84866732351     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2012.08.009     Document Type: Article

References (40)

1. O. Sporns, D.R. Chialvo, M. Kaiser, and C.C. Hilgetag Organization, development and function of complex brain networks TRENDS Cogn. Sci. 8 9 2004 419 425
2. D.S. Bassett, A.M. Lindenberg, S. Achard, T. Duke, and E. Bullmore Adaptive reconfiguration of fractal small-world human brain functional networks Proc. Natl. Acad. Sci. USA 103 19518 2006
3. L. Zemanová, C. Zhou, and J. Kurths Structural and functional clusters of complex brain networks Physica D 224 2006 202 212
4. K.V. Srinivas, R. Jain, S. Saurav, and S.K. Sikdar Small-world network topology of hippocampal neuronal network is lost, in an in vitro glutamate injury model of epilepsy Eur. J. Neurosci. 25 2007 3276 3286
5. A.L. Barabási, and R. Albert Emergence of scaling in random networks Science 286 1999 509 512
6. R. Albert, and A.L. Barabási Statistical mechanics of complex networks Rev. Mod. Phys. 74 2002 47 97
7. F. Sorrentino, M. di Bernardo, G. Huerta Cuéllar, and S. Boccaletti Synchronization in weighted scale-free networks with degree-degree correlation Physica D 224 2006 123 129
8. A. Arenas, A. Díaz-Guilera, and C.J. Pérez-Vicente Synchronization processes in complex networks Physica D 224 2006 27 34
9. A. Arenas, A. Diaz, J. Kurths, Y. Moreno, and C. Zhou Synchronization in complex networks Phys. Rep. 469 2008 93 153
10. D. Huang, and G. Pipa Achieving synchronization of networks by an auxiliary hub EPL 77 50010 2007
11. N. Masuda, and N. Konno VIP-club phenomenon: emergence of elites and masterminds in social networks Social Networks 28 2006 297 309
12. H. Kitajima, and J. Kurths Bifurcation in neuronal networks with hub structure Physica A 388 2009 4499 4508
13. P. Bonifazi, M. Goldin, M.A. Picardo, A. Cattani, G. Bianconi, A. Represa, Y. Ben-Ari, and R. Cossart GABAergic hub neurons orchestrate synchrony in developing hippocampal networks Science 326 2009 1419 1424
14. P.N. McGraw, and M. Menzinger Topology and computational performance of attractor neural networks Phys. Rev. E 68 047102 2003
15. D. Terman, and D. Wang Global competition and local cooperation in a network of neural oscillators Physica D 81 1995 148 176
16. R. Borisyuk, Y. Kazanovich, D. Chik, V. Tikhanoff, and A. Cangelosi A neural model of selective attention and object segmentation in the visual scene: an approach based on partial synchronization and star-like architecture Neural Netw. 22 2009 707 719
17. Y.B. Kazanovich, and R.M. Borisyuk Dynamics of neural networks with a central element Neural Netw. 12 1999 441 454
18. D. Chik, R. Borisyuk, and Y. Kazanovich Selective attention model with spiking elements Neural Netw. 22 2009 890 900
19. O. Burylko, Y. Kazanovich, and R. Borisyuk Bifurcation in phase oscillator networks with a central element Physica D 24 2012 1027 1089
20. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon Network motifs: simple building blocks of complex networks Science 298 2002 824 827
21. M. Barahona, and L.M. Pecora Synchronization in small-world systems Phys. Rev. Lett. 89 054101 2002
22. N. Takahashi, T. Sasaki, W. Matsumoto, and Y. Ikegaya Circuit topology for synchronizing neurons in spontaneously active networks Proc. Natl. Acad. Sci. USA 107 22 2010 10244 10249
23. E. Bullmore, and O. Sporns Complex brain networks: graph theoretical analysis of structural and functional systems Nat. Rev. Neurosci. 10 2009 186 198
24. A. Pikovsky, M. Rosenblum, and J. Kurths Synchronization: A Universal Concept in Nonlinear Sciences 2001 Cambridge University Press
25. R. Ochi, E. Ioka, H. Kitajima, Synchronization in synaptically coupled neurons with hub structure, in: Proc. NOLTA'08, 2008, pp. 345-348.
26. C. Morris, and H. Lecar Voltage oscillations in the barnacle giant muscle fiber Biophys. J. 35 1981 193 213
27. A.L. Hodgkin, and A.F. Huxley A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 1952 500 544
28. K. Yoshikawa, S. Maeda, and H. Kawakami Various oscillatory regimes and bifurcations in a dynamic chemical system at an interface Ferroelectrics 86 1988 281 298
29. T. Yoshinaga, H. Kawakami, and K. Yoshikawa A circuit metaphor for nonlinear oscillation in a chemical system at a water-oil interface Trans. IEICE j71-A 10 1988 1843 1851
30. M. Golubitsky, I. Stewart, and D.G. Schaeffer Singularities and Groups in Bifurcation Theory II 1988 Springer-Verlag New York
31. Y.A. Kuznetsov Elements of Applied Bifurcation Theory 1995 Springer-Verlag New York
32. K. Tsumoto, H. Kitajima, T. Yoshinaga, K. Aihara, and H. Kawakami Bifurcations in Morris-Lecar neuron model Neurocomputing 69 4-6 2006 293 316
33. M. Nomura, T. Fukai, and T. Aoyagi Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses Neural Comput. 15 2003 2179 2198
34. Q. Wang, Q. Lu, and G. Chen Synchronization transition induced by synaptic delay in coupled fast-spiking neurons Internat. J. Bifur. Chaos 18 4 2008 1189 1198
35. E.M. Izhikevich Synchronization of elliptic bursters SIAM Rev. 43 2 2001 315 344
36. T. Yoshinaga, Y. Sano, and H. Kawakami A method to calculate bifurcations in synaptically coupled Hodgkin-Huxley equations Internat. J. Bifur. Chaos 9 7 1999 1451 1458
37. H. Kitajima, and H. Kawakami Bifurcation and chaos of synchronized states in oscillators with hard characteristics and state coupling Internat. J. Bifur. Chaos 12 5 2002 1199 1206
38. H. Kitajima, T. Yoshinaga, H. Kawakami, Synchronization in two coupled oscillators with three ports, in: Proc. NOLTA'94, 1994, pp. 89-92.
39. H. Kawakami Bifurcation of periodic responses in forced dynamic nonlinear circuits: computation of bifurcation values of the system parameters IEEE Trans. Circuits Syst. CAS-31 3 1984 246 260
40. O. Papy, and H. Kawakami Symmetry breaking and recovering in a system of n hybridly coupled oscillators IEICE Trans. Fundam. E79-A 10 1996 1568 1574