Dynamics-based scalability of complex networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 4, 2008, Pages

  Huang, Liang ^a   Lai, Ying Cheng ^a,b   Gatenby, Robert A ^c  

^a Arizona State University   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; ELECTRIC NETWORK TOPOLOGY; SCALABILITY;

COMPLEX NETWORKS; COUPLED NETWORKS; DYNAMICAL PROPERTIES; NETWORK SCALABILITIES; NETWORK SIZES; NETWORK TOPOLOGIES; RANDOM NETWORKS; REGULAR NETWORKS; SCALE-FREE NETWORKS; SYNCHRONIZABILITY; TECHNOLOGICAL NETWORKS;

TOPOLOGY;

EID: 55849139400     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.045102     Document Type: Article

References (18)

1. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
2. P. Erdös and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960);
3. B. Bollobaás, Random Graphs (Academic, London, 1985).
4. D. J. Watts and S. H. Strogatz, Nature (London) 10.1038/30918 393, 440 (1998).
5. A.-L. Barabási and R. Albert, Science 10.1126/science.286.5439.509 286, 509 (1999).
6. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 10.1103/PhysRevLett.80. 2109 80, 2109 (1998).
7. See, for example, L. F. Lago-Fernandez, R. Huerta, F. Corbacho, and J. A. Siguenza, Phys. Rev. Lett. 10.1103/PhysRevLett.84.2758 84, 2758 (2000);
8. X. F. Wang and G. Chen, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 187 (2002);
9. X. F. Wang and G. Chen, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 10.1109/81.974874 49, 54, (2002);
10. M. Barahona and L. M. Pecora, Phys. Rev. Lett. 10.1103/PhysRevLett.89. 054101 89, 054101 (2002);
11. T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. C. Hoppensteadt, Phys. Rev. Lett. 10.1103/PhysRevLett.91.014101 91, 014101 (2003);
12. A. E. Motter, C. Zhou, and J. Kurths, Europhys. Lett. 10.1209/epl/i2004-10365-4 69, 334 (2005);
13. M. Chavez, D.-U. Hwang, A. Amann, H. G. E. Hentschel, and S. Boccaletti, Phys. Rev. Lett. 10.1103/PhysRevLett.94.218701 94, 218701 (2005).
14. In relation to biological systems, we have calculated MSFs for a Hindmarsh-Rose neuron using parameters and coupling functions from M. Dhamala, V. K. Jirsa, and M. Ding [Phys. Rev. Lett. 10.1103/PhysRevLett.92.028101 92, 028101 (2004)], which also fits in our classification: 21 coupling belongs to class-I dynamics; 11, 12, and 22 couplings belong to class-II dynamics; and all other coupling schemes do not give a negative Ψ (K) region. 10.1103/PhysRevLett.92.028101
15. A. Pikovsky, A. Zaikin, and M. A. de la Casa, Phys. Rev. Lett. 10.1103/PhysRevLett.88.050601 88, 050601 (2002).
16. E. P. Wigner, Ann. Math. 10.2307/1969342 53, 36 (1951);
17. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981). 10.1103/RevModPhys.53.385
18. D.-H. Kim and A. E. Motter, Phys. Rev. Lett. 10.1103/PhysRevLett.98. 248701 98, 248701 (2007).