Delayed feedback control of bursting synchronization in a scale-free neuronal network

Neural Networks

Volumn 23, Issue 1, 2010, Pages 114-124

  Batista, C A S ^a   Lopes, S R ^a   Viana, R L ^a   Batista, A M ^b  

^a FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^b STATE UNIVERSITY OF PONTA GROSSA   (Brazil)

Author keywords

Bursting; Control; Feedback; Scale free network; Synchronization

Indexed keywords

BURSTING NEURONS; COLLECTIVE OSCILLATIONS; CONTROL FEEDBACK; DEEP BRAIN STIMULATION; DELAYED FEEDBACK CONTROL; ESSENTIAL TREMOR; LOCAL DYNAMICS; MEAN-FIELD; NEUROLOGICAL DISEASE; NEURONAL NETWORKS; PARKINSON'S DISEASE; PERTURBATION STRENGTH; POWER LAW DISTRIBUTION; SCALE FREE NETWORKS; SCALE-FREE; SCALE-FREE PROPERTIES; SIMPLIFIED MODELS; SYNCHRONIZED OSCILLATIONS; TIME-SCALES;

DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; NEURAL NETWORKS; SIGNAL ENCODING; SYNCHRONIZATION;

FEEDBACK;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BRAIN DEPTH STIMULATION; CONTROLLED STUDY; ESSENTIAL TREMOR; FEEDBACK SYSTEM; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MEDICAL RESEARCH; NERVE CELL STIMULATION; NEUROLOGIC DISEASE; OSCILLATION; PARKINSON DISEASE; PRIORITY JOURNAL; SIGNAL PROCESSING; SPIKE WAVE; TIME;

ACTION POTENTIALS; ANIMALS; FEEDBACK, PHYSIOLOGICAL; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL INHIBITION; NEURAL NETWORKS (COMPUTER); NEURONS; NONLINEAR DYNAMICS; PERIODICITY; PROBABILITY; REACTION TIME; TIME FACTORS;

EID: 70649088864     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2009.08.005     Document Type: Article

References (62)

1. Acebrón J.A., Bonilla L.L., Vicente C.J.P., Ritort F., and Spigler R. The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics 77 January (2005) 137-185
2. Achacoso T.B., and Yamamoto W.S. AY's neuroanatomy of C. elegans for computation (1991), CRC Press, Boca Raton, FL, USA
3. Achard S., Salvador R., Whitcher B., Suckling J., and Bullmore E. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience 4 January (2006) 63-72
4. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Reviews of Modern Physics 74 January (2002) 47-97
5. Baiesi M., and Paczuski M. Scale-free networks of earthquakes and aftershocks. Physical Review E 69 066106 (2004) 1-8
6. Barabási A.-L., and Albert R. Emergence of scaling in random networks. Science 286 October (1999) 509-512
7. Barabási A.-L., Albert R., and Jeong H. Scale-free characteristics of random networks: The topology of the world-wide web. Physica A: Statistical Mechanics and its Applications 281 June (2000) 69-77
8. Barabási A.-L., and Oltvai Z.N. Network biology: Understanding the cell's functional organization. Nature Reviews Genetics 5 February (2004) 101-113
9. Batista C.A.S., Batista A.M., Pinto S.E.d.S., Viana R.L., Lopes S.R., and Caldas I.L. Direction coherence in scale-free lattices of chaotic maps. Physica A 383 (2007) 725-732
10. Batista C.A.S., Batista A.M., de Pontes J.A.C., Viana R.L., and Lopes S.R. Chaotic phase synchronization in scale-free networks of bursting neurons. Physical Review E 76 016218 (2007) 1-10
11. Bear M.F., Connors B.W., and Paradiso M.A. Neuroscience: Exploring the brain. 2nd ed. (2002), Lippincott Williams & Wilkins, Philadelphia, PA, USA
12. Belykh I., de Lange E., and Hasler M. Synchronization of bursting neurons: What matters in the network topology. Physical Review Letters 94 188101 (2005) 1-4
13. Benabid A.L., Pollak P., Gervason C., Hoffmann D., Gao D.M., Hommel M., et al. Long-term suppression of tremor by chronic stimulation of the ventral intermediate thalamic nucleus. Lancet 337 February (1991) 403-406
14. Blond S., Caparros-Lefevre D., Parker F., Assaker R., Petit H., Guieu J.-D., et al. Control of tremor and involuntary movement disorders by chronic stereotactic stimulation of the ventral intermediate thalamic nucleus. Journal of Neurosurgery 77 (1992) 62-68
15. Broder A., Kumar R., Maghoul F., Raghavan P., Rajagopalan S., Stata R., et al. Graph structure in the web. Computer Networks 33 June (2000) 309-320
16. In: Borhnoldt S., and Schuster H.G. (Eds). Handbook of graphs and networks (2003), Wiley-VCH Verlag, New York
17. Chialvo D.R. Critical brain networks. Physica A 340 September (2004) 756-765
18. Cumin D., and Unsworth C.P. Generalizing the Kuramoto model for the study of neuronal synchronisation in the brain. Physica D 226 February (2007) 181-196
19. de Moura A.P.S., Lai Y.-C., and Motter A.E. Signatures of small-world and scale-free properties in large computer programs. Physical Review E 68 017102 (2003) 1-4
20. Dayan P., and Abbott L.F. Theoretical neuroscience: Computational and mathematical modeling of neural systems (2001), MIT Press, Cambridge, MA, USA
21. Dhamala M., Jirsa V.K., and Ding M. Transitions to synchrony in coupled bursting neurons. Physical Review Letters 92 028101 (2004) 1-4
22. Dorogovtsev S.N., and Mendes J.F.F. Evolution of networks. Advances in Physics 51 (2002) 1079-1187
23. Equiluz V.M., Chialvo D.R., Cecchi G.A., Buliki M., and Apkarian A.V. Scale-free brain functional networks. Physical Review Letters 94 018102 (2005) 1-4
24. Hagmann P., Cammoun L., Gigandet X., Meuli R., Honey C.J., Wedeen V.J., and Sporns O. Mapping the structural core of human cerebral cortex. PLoS Biology 6 July (2008) 1479-1483
25. Hindmarsh J.L., and Rose R.M. A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London, Series B 221 (1984) 87-102
26. Humphries M.D., Gurney K., and Prescott T.J. The brainstem reticular formation is a small-world, not scale-free, network. Proceedings of the Royal Society (London) B 273 February (2006) 503-511
27. Hodgkin A.L., and Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117 (1952) 500-544
28. Honey C.J., Sporns O., Cammoun L., Gigandet X., Thiran J.P., Meulic R., et al. Predicting human resting-state functional connectivity from structural connectivity. Proceedings of the Natural Academy of Sciences (USA) 106 February (2009) 2035-2040
29. Ivanchenko M.V., Osipov G.V., Shalfeev V.D., and Kurths J. Phase synchronization in ensembles of bursting oscillators. Physical Review Letters 93 134101 (2004) 1-4
30. Jeong H., Tombor B., Albert R., Oltvai Z.N., and Barabási A.-L. The large-scale organization of metabolic networks. Nature 407 October (2000) 651-654
31. Jeong H., Mason S.P., Barabási A.-L., and Oltvai Z.N. Lethality and centrality in protein networks. Nature 411 May (2001) 41-42
32. Kuramoto Y. Chemical oscillations, waves, and turbulence (1984), Dover Publications, New York
33. Lijeros F., Edling C.R., Amaral L.A.N., Stanley H.E., and Aberg Y. The web of human sexual contacts. Nature 411 (2001) 907-908
34. López-Ruiz R., Moreno Y., Pacheco A.F., Boccaletti S., and Hwang D.-U. Awaking and sleeping of a complex network. Neural Network 20 (2007) 102-108
35. Maistrenko Y.L., Popovych O.V., and Tass P.A. In: Chazottes J.-R., and Fernandez B. (Eds). Dynamics of coupled map lattices and of related spatially extended systems. Lecture notes in physics Vol. 671 (2005), Springer Verlag, Berlin-Heidelber
36. In: Milton J., and Jung P. (Eds). Epilepsy as a dynamic disease (2003), Springer Verlag, Berlin
37. Mirollo R.E., and Strogatz S.H. Synchronization of pulse-coupled biological oscillators. SIAM Journal of Applied Mathematics 50 December (1990) 1645-1662
38. Nini A., Feingold A., Slovin H., and Bergman H. Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. Journal of Neurophysiology 74 (1995) 1800-1805
39. Newman M.E.J., and Watts D. Scaling and percolation in the small-world network model. Physical Review E 60 (1999) 7332-7342
40. Newman M.E.J., and Watts D. Renormalization group analysis of the small-world network model. Physics Letters A 263 December (1999) 341-346
41. Pastor-Satorras R., Vázquez A., and Vespignani A. Dynamical and correlation properties of the internet. Physical Review Letters 87 258701 (2001) 1-4
42. Pastor-Satorras R., and Vespignani A. Epidemic spreading in scale-free networks. Physical Review Letters 86 October (2001) 3200-3203
43. Perotti J.I., Tamarit F.A., and Cannas S.A. A scale-free neural network for modelling neurogenesis. Physica A Statistical Mechanics and its Applications 371 November (2006) 71-75
44. Piekniewski F., and Schreiber T. Spontaneous scale-free structure of spike flow graphs in recurrent neural networks. Neural Networks 21 December (2008) 1530-1536
45. Pikovsky A.S., Rosenblum M.G., and Kurths J. Synchronization: A universal concept in nonlinear sciences (2003), Cambridge University Press, Cambridge
46. Rosenblum M.G., and Pikowsky A.S. Delayed feedback control of collective synchrony: An approach to suppression of pathological brain rhythms. Physical Review E 70 041904 (2004) 1-11
47. Rosenblum M.G., and Pikowsky A.S. Controlling synchronization in an ensemble of globally coupled oscillators. Physical Review Letters 92 114102 (2004) 1-4
48. Roy R., and Thornbert Jt. K.S. Experimental synchronization of chaotic lasers. Physical Review Letters 72 August (1994) 2009-2012
49. Rulkov N.F. Regularization of synchronized chaotic bursts. Physical Review Letters 86 August (2001) 183-186
50. Rulkov N.F. Modeling of spiking-bursting neural behavior using two-dimensional map. Physical Review E 65 041922 (2002) 1-9
51. Rulkov N.F., Timofeev I., and Bazhenov M. Oscillations in large-scale cortical networks: Map-based model. Journal of Computational Neuroscience 17 September (2004) 203-223
52. Scannell J.W., and Young M.P. The connectional organization of neural systems in the cat cerebral cortex. Current Biology 3 April (1993) 191-200
53. Sporns O. In: R. K. (Ed). Neuroscience databases: A practical guide (2002), Kluwer Publishers, Boston 169
54. Sporns O., Chialvo D.R., Kaiser M., and Hilgetag C.C. Organization, development and function of complex brain networks. Trends in Cognitive Sciences 8 September (2004) 418-425
55. Stauffer D., Aharony A., da Fontoura Costa L., and Adler J. Efficient Hopfield pattern recognition on a scale-free neural network. The European Physical Journal B 32 (2003) 395-399
56. Thomson A.M. Neurotransmission: Chemical and electrical interneuron coupling. Current Biology 10 February (2000) R110-R112
57. van der Heuvel M.P., Stam C.J., Boersma M., and Hulshoff Pol H.E. Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain. NeuroImage 43 August (2008) 528-539
58. Watts D.J. Small worlds (2000), Princeton University Press, Princeton, NJ, USA
59. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 6684 (1998) 440-442
60. Wiesenfeld K., Colet P., and Strogatz S.H. Synchronization transitions in a disordered Josephson series array. Physical Review Letters 76 July (1996) 404-407
61. Wuchty S. Scale-free behavior in protein domain networks. Molecular Biology and Evolution 18 (2001) 1694-1702
62. Zhou C., Zemanová L., Zamora G., Hilgetag C.C., and Kurths J. Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letters 97 238103 (2006) 1-4