Unstable dynamics, nonequilibrium phases, and criticality in networked excitable media

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

Volumn 82, Issue 4, 2010, Pages

  De Franciscis, S ^a   Torres, J J ^a   Marro, J ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

1/F NOISE; ATTRACTOR SPACES; CONDENSED MATTER SYSTEM; CONNECTION WEIGHTS; CORTICAL NETWORK; CRITICAL STATE; EXCITABLE MEDIA; EXCITABLE SYSTEMS; NON-EQUILIBRIUM PHASIS; PHASE REGION; POWER LAW DISTRIBUTION; TIME-SCALES; UNSTABLE DYNAMICS;

BEHAVIORAL RESEARCH; CRITICAL CURRENT DENSITY (SUPERCONDUCTIVITY); CRITICALITY (NUCLEAR FISSION); MATHEMATICAL MODELS; SCALES (WEIGHING INSTRUMENTS);

COMPUTER SIMULATION;

EID: 77957579736     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.041105     Document Type: Article

References (62)

1. D. O. Hebb, The Organization of Behavior: A Neurophysiological Theory (Wiley, New York, 1949).
2. S. Amari, IEEE Trans. Comput. C-21, 1197 (1972). 10.1109/T-C.1972.223477
3. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982). 10.1073/pnas.79.8.2554
4. D. J. Amit, Modeling Brain Function: The World of Attractor Neural Networks (Cambridge University Press, Cambridge, 1989).
5. J. Marro, P. L. Garrido, and J. J. Torres, Phys. Rev. Lett. 81, 2827 (1998). 10.1103/PhysRevLett.81.2827
6. J. M. Cortes, P. L. Garrido, H. J. Kappen, J. Marro, C. Morillas, D. Navidad, and J. J. Torres, Algorithms for Identification and Categorization, AIP Conf. Proc. No. 779 (AIP, New York, 2005), p. 178.
7. T. J. Wills, C. Lever, F. Cacucci, N. Burgess, and J. O'Keefe, Science 308, 873 (2005). 10.1126/science.1108905
8. M. Rabinovich, R. Huerta, and G. Laurent, Science 321, 48 (2008). 10.1126/science.1155564
9. M. O. Magnasco, O. Piro, and G. A. Cecchi, Phys. Rev. Lett. 102, 258102 (2009). 10.1103/PhysRevLett.102.258102
10. T. Petermann, T. C. Thiagarajan, M. Lebedev, M. Nicolelis, D. R. Chialvo, and D. Plenz, Proc. Natl. Acad. Sci. U.S.A. 106, 15921 (2009). 10.1073/pnas.0904089106
11. E. Thelen and L. B. Smith, A Dynamic Systems Approach to the Development of Cognition and Action (The MIT Press, Cambridge, MA, 1994).
12. W. J. Freeman, Neural Networks 13, 11 (2000). 10.1016/S0893-6080(99) 00093-3
13. H. Korn and P. Faure, C. R. Biol. 326, 787 (2003). 10.1016/j.crvi.2003. 09.011
14. K. Kaneko and I. Tsuda, Chaos 13, 926 (2003). 10.1063/1.1607783
15. J. S. Perkimki, T. H. Makikallio, and H. V. Huikuri, Clin. Exp. Hypertens. 27, 149 (2005). 10.1081/CEH-48742
16. M. Shen, G. Chang, S. Wang, and P. J. Beadle, Lecture Notes in Computation Science 3973, 560 (2006). 10.1007/11760191-82
17. L. M. Jones, A. Fontanini, B. F. Sadacca, P. Miller, and D. B. Katz, Proc. Natl. Acad. Sci. U.S.A. 104, 18772 (2007). 10.1073/pnas.0705546104
18. M. I. Rabinovich and M. K. Muezzinoglu, Phys. Usp. 53, 357 (2010). 10.3367/UFNe.0180.201004b.0371
19. H. Sompolinsky, A. Crisanti, and H. J. Sommers, Phys. Rev. Lett. 61, 259 (1988). 10.1103/PhysRevLett.61.259
20. M. Adachi and K. Aihara, Neural Networks 10, 83 (1997). 10.1016/S0893-6080(96)00061-5
21. H. Bersini and P. Sener, Neural Networks 15, 1197 (2002). 10.1016/S0893-6080(02)00096-5
22. H. Lu, Phys. Lett. A 298, 109 (2002). 10.1016/S0375-9601(02)00538-8
23. X. S. Yang and Q. Yuan, Neurocomputing 69, 232 (2005). 10.1016/j.neucom.2005.06.005
24. W. Freeman and M. D. Holmes, Neural Networks 18, 497 (2005). 10.1016/j.neunet.2005.06.014
25. C. Molter, U. Salihoglu, and H. Bersini, Neural Comput. 19, 80 (2007). 10.1162/neco.2007.19.1.80
26. W.-Z. Huang and Y. Huang, Appl. Math. Comput. 206, 1 (2008). 10.1016/j.amc.2008.08.041
27. J. Marro, J. J. Torres, and J. M. Cortes, J. Stat. Mech.: Theory Exp. (2008), P02017. 10.1088/1742-5468/2008/02/P02017
28. J. J. Torres, J. Marro, J. M. Cortes, and B. Wemmenhove, Neural Networks 21, 1272 (2008). 10.1016/j.neunet.2008.07.002
29. O. Mazor and G. Laurent, Neuron 48, 661 (2005). 10.1016/j.neuron.2005.09. 032
30. J. Marro and R. Dickman, Nonequilibrium Phase Transitions and Critical Phenomena in Lattice Systems (Cambridge University Press, Cambridge, 2005).
31. J. J. Torres, P. L. Garrido, and J. Marro, Phys. Rev. B 58, 11488 (1998). 10.1103/PhysRevB.58.11488
32. Y. Bar-Yam, D. Harmon, and B. de Bivort, Science 323, 1016 (2009). 10.1126/science.1163225
33. O. Hallatschek and D. R. Nelson, Phys. Today 62 (7), 42 (2009). 10.1063/1.3177227
34. A. Diaz-Guilera and E. R. Alvarez-Buylla, in Handbook on Biological Networks, Lecture Notes in Complex Systems, edited by, S. Boccaletti, V. Latora, and, Y. Moreno, (World Scientific, Singapore, 2009), Vol. 10.
35. J. T. Sun, S. J. Wang, Z. G. Huang, L. Yang, Y. Do, and Y. H. Wang, New J. Phys. 12, 063034 (2010). 10.1088/1367-2630/12/6/063034
36. D. R. Chialvo, Physica A 340, 756 (2004). 10.1016/j.physa.2004.05.064
37. V. M. Eguíluz, D. R. Chialvo, G. A. Cecchi, M. Baliki, and A. V. Apkarian, Phys. Rev. Lett. 94, 018102 (2005). 10.1103/PhysRevLett.94.018102
38. W. J. Freeman, M. D. Holmes, A. West, and S. Vanhatalo, Clin. Neurophysiol. 117, 1228 (2006). 10.1016/j.clinph.2006.03.012
39. D. R. Chialvo, P. Balenzuela, and D. Fraiman, Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (AIP, New York, 2008).
40. J. A. Bonachela, S. de Franciscis, J. J. Torres, and M. A. Muñoz, J. Stat. Mech.: Theory Exp. (2010), P02015. 10.1088/1742-5468/2010/02/P02015
41. D. Plenz and D. Chialvo, e-print arXiv:0912.5369.
42. D. Millman, S. Mihalas, A. Kirkwood, and E. Niebur, Nat. Phys. 6, 801 (2010). 10.1038/nphys1757
43. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. 81, 3088 (1984) 10.1073/pnas.81.10.3088
44. W. S. McCulloch and W. Pitts, Bull. Math. Biophys. 5, 115 (1943) 10.1007/BF02478259
45. M. E. J. Newman, SIAM Rev. 45, 167 (2003) 10.1137/S003614450342480
46. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Phys. Rep. 424, 175 (2006). 10.1016/j.physrep.2005.10.009
47. S. Johnson, J. Marro, and J. J. Torres, EPL 83, 46006 (2008). 10.1209/0295-5075/83/46006
48. J. M. Cortes, J. J. Torres, J. Marro, P. L. Garrido, and H. J. Kappen, Neural Comput. 18, 614 (2006). 10.1162/neco.2006.18.3.614
49. J. Mejias, H. Kappen, and J. Torres, e-print arXiv:1007.3556, PLoS One (to be published).
50. D. J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. Lett. 55, 1530 (1985) 10.1103/PhysRevLett.55.1530
51. D. J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. A 32, 1007 (1985). 10.1103/PhysRevA.32.1007
52. M. Griniasty, M. V. Tsodyks, and D. J. Amit, Neural Comput. 5, 1 (1993). 10.1162/neco.1993.5.1.1
53. J. Csicsvari, D. A. Henze, B. Jamieson, K. D. Harris, A. Sirota, P. Baethó, K. D. Wise, and G. Buzsáki, J. Neurophysiol. 90, 1314 (2003). 10.1152/jn.00116.2003
54. M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, Rev. Mod. Phys. 65, 413 (1993). 10.1103/RevModPhys.65.413
55. See, however, Ref. for an important concern on temporal and spatial resolutions.
56. D. Kaplan and L. Glass, Understanding Nonlinear Dynamics (Springer, New York, 1995).
57. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge, MA, 2007).
58. R. FitzHugh, Bull. Math. Biophys. 17, 257 (1955) 10.1007/BF02477753
59. R. FitzHugh, Biophys. J. 1, 445 (1961) 10.1016/S0006-3495(61)86902-6
60. J. Nagumo, S. Yoshizawa, and S. Arimoto, IEEE Trans. Commun. Technol. 12, 400 (1965).
61. T. D. Rogers and D. C. Whitley, Math. Modell. 4, 9 (1983). 10.1016/0270-0255(83)90030-1
62. J. Hertz, A. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, MA, 1991).