Analytical investigation of self-organized criticality in neural networks

Journal of the Royal Society Interface

Volumn 10, Issue 78, 2013, Pages

  Droste, Felix ^a   Do, Anne Ly ^b   Gross, Thilo ^c  

^a BERNSTEIN CENTER FOR COMPUTATIONAL NEUROSCIENCE   (Germany)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Adaptive network; Neural network; Self organized criticality

Indexed keywords

CRITICALITY (NUCLEAR FISSION); DATA PROCESSING; DYNAMICAL SYSTEMS; DYNAMICS; STOCHASTIC MODELS;

ACTIVITY-DEPENDENT; ADAPTIVE NETWORKS; ANALYTICAL INVESTIGATIONS; DYNAMICAL PHASE TRANSITION; LOW-DIMENSIONAL REPRESENTATION; MACROSCOPIC DYNAMICS; NUMERICAL EVIDENCE; PLAUSIBLE MECHANISMS; SELF-ORGANIZED CRITICALITY; STEADY STATE; STOCHASTIC DYNAMICS; SYNAPTIC PLASTICITY; TRANSCRITICAL BIFURCATION;

NEURAL NETWORKS;

ARTICLE; DYNAMICAL CRITICALITY; HEMOSTASIS; MATHEMATICAL MODEL; NERVE CELL; NERVE CELL PLASTICITY; NERVOUS SYSTEM PARAMETERS; NEUROTRANSMISSION; PHASE TRANSITION; STOCHASTIC MODEL; ANIMAL; BIOLOGICAL MODEL; HUMAN; NERVE CELL NETWORK; PHYSIOLOGY; SYNAPSE;

ANIMALS; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; SYNAPSES;

EID: 84871302851     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2012.0558     Document Type: Article

References (44)

1. Langton CG. 1990 Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42, 12-37. (doi:10.1016/0167-2789(90)90064-V)
2. Kinouchi O, Copelli M. 2006 Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2, 348-351. (doi:10.1038/nphys289)
3. Legenstein R, Maass W. 2007 Edge of chaos and prediction of computational performance for neural circuit models. Neural Networks 20, 323-334. (doi:10.1016/j.neunet.2007.04.017)
4. Camalet S, Duke T, Jülicher F, Prost J. 2009 Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl Acad. Sci. USA 97, 3183-3188. (doi:10.1073/pnas.97.7.3183)
5. Beggs JM. 2008 The criticality hypothesis: how local cortical networks might optimize information processing. Phil. Trans. R. Soc. A 366, 329. (doi:10.1098/rsta.2007.2092)
6. Beggs JM, Plenz D. 2003 Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11 167-11 177.
7. Beggs JM, Plenz D. 2004 Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216-5229. (doi:10.1523/JNEUROSCI.0540-04.2004)
8. Plenz D, Thiagarajan TC. 2007 The organizing principles of neuronal avalanches: cell assemblies in the cortex? Trends Neurosci. 30, 101-110. (doi:10.1016/j.tins.2007.01.005)
9. Novikov E, Novikov A, Shannahoff-Khalsa D, Schwartz B, Wright J. 1997 Scale-similar activity in the brain. Phys. Rev. E 56, 2387-2389. (doi:10.1103/PhysRevE.56.R2387)
10. Freeman WJ, Rogers LJ, Holmes MD, Silbergeld DL. 2000 Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands. J. Neurosci. Methods 95, 111-121. (doi:10.1016/S0165-0270(99)00160-0)
11. Meisel C, Storch A, Hallmeyer-Elgner S, Bullmore E, Gross T. 2012 Failure of adaptive self-organized criticality during epileptic seizure attacks. PLoS Comput. Biol. 8, e10023122012. (doi:10.1371/journal.pcbi.1002312)
12. Kitzbichler MG, Smith ML, Christensen SR, Bullmore E. 2009 Broadband criticality of human brain network synchronization. PLoS Comput. Biol. 5, e1000314. (doi:10.1371/journal.pcbi.1000314)
13. Gross T, Blasius B. 2008 Adaptive coevolutionary networks: a review. J. R. Soc. Interface 5, 259-271. (doi:10.1098/rsif.2007.1229)
14. Gross T, Sayama H. (eds) 2009 Adaptive networks - theory, models and applications. Heidelberg, Germany: Springer.
15. Christensen K, Donangelo R, Koiller B, Sneppen K. 1998 Evolution of random networks. Phys. Rev. Lett. 81, 2380-2383. (doi:10.1103/PhysRevLett.81. 2380)
16. Bornholdt S, Rohlf T. 2000 Topological evolution of dynamical networks: global criticality from local dynamics. Phys. Rev. Lett. 84, 6114-6117. (doi:10.1103/PhysRevLett.84.6114)
17. Ebel H, Bornholdt S. 2002 Evolutionary games and the emergence of complex networks. (http://arxiv.org/abs/cond-mat/0211666).
18. Bornholdt S, Röhl T. 2003 Self-organized critical neural networks. Phys. Rev. E 67, 066118. (doi:10.1103/PhysRevE.67.066118)
19. Levina A, Herrmann JM, Geisel T. 2007 Dynamical synapses causing self-organized criticality in neural networks. Nat. Phys. 3, 857-860. (doi:10.1038/nphys758)
20. Burda Z, Krzywicki A, Martin OC. 2008 Adaptive networks of trading agents. Phys. Rev. E 78, 046106. (doi:10.1103/PhysRevE.78.046106)
21. Levina A, Herrmann JM, Geisel T. 2009 Phase transitions towards criticality in a neural system with adaptive interactions. Phys. Rev. Lett. 102, 118110. (doi:10.1103/PhysRevLett.102.118110)
22. Meisel C, Gross T. 2009 Adaptive self-organization in a realistic neural network model. Phys. Rev. E 80, 061917. (doi:10.1103/PhysRevE.80.061917)
23. MacArthur BD, Sánchez-García RJ, Ma'ayan A. 2010 Microdynamics and criticality of adaptive regulatory networks. Phys. Rev. Lett. 104, 168701. (doi:10.1103/PhysRevLett.104.168701)
24. ITRS. 2009 International technology roadmap for semiconductors. See http://www.itrs.net/reports.html.
25. Jo SH, Chang T, Ebong I, Bhadviya BB, Mazumder P, Lu W. 2010 Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297-1301. (doi:10.1021/nl904092h)
26. Gross T, D'Lima CJD, Blasius B. 2006 Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 96, 208701. (doi:10.1103/PhysRevLett.96.208701)
27. Chua LO. 1971 Memristor: the missing circuit element. IEEE Trans. Circuit Theory. 18, 507-519. (doi:10.1109/TCT.1971.1083337)
28. Turrigiano GG, Leslie KR, Desai NS, Rutherford LC, Nelson SB. 1998 Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature 391, 892-895. (doi:10.1038/36103)
29. Turrigiano GG, Nelson SB. 2004 Homeostatic plasticity in the developing nervous system. Nat. Rev. Neurosci. 5, 97-107. (doi:10.1038/nrn1327)
30. Anderson RM, May RM. 1991 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
31. Bauch CT. 2005 The spread of infectious diseases in spatially structured populations: an invasory pair approximation. Math. Biosci. 198, 217-237. (doi:10.1016/j.mbs.2005.06.005)
32. Zschaler G, Böhme G, Seißinger M, Huepe C, Gross T. 2012 Early fragmentation in the adaptive voter model on directed networks. Phys. Rev. E 85, 046107. (doi:10.1103/PhysRevE.85.046107)
33. Kuznetsov YA. 1998 Elements of applied bifurcation theory. New York, NY: Springer.
34. Gradshteyn IS, Ryzhik IM. 2007 Routh-Hurwitz theorem. In Tables of integrals, series, and products (eds A Jeffrey, D Zwillinger), p. 1086, 7th edn. San Diego, CA: Academic Press.
35. Doedel E et al. 2007 AUTO 97 - Continuation and bifurcation software for ordinary differential equations. Department of Computer Science, Concordia University, Montreal.
36. Desai NS, Rutherford LC, Turrigiano GG. 1999 Plasticity in the intrinsic excitability of cortical pyramidal neurons. Nat. Neurosci. 2, 515-520. (doi:10.1038/9165)
37. Losonczy A, Makara JK, Magee JC. 2008 Compartmentalized dendritic plasticity and input feature storage in neurons. Nature 452, 436-441. (doi:10.1038/nature06725)
38. Vespignani A, Zapperi S. 1998 How self-organized criticality works: a unified mean-field picture. Phys. Rev. E 57, 6345-6362. (doi:10.1103/PhysRevE. 57.6345)
39. Dickman R, Munoz M, Vespignani A, Zapperi S. 2000 Paths to self-organized criticality. Braz. J. Phys. 30, 27-41. (doi:10.1590/S0103-97332000000100004)
40. Bonachela JA, Muñoz MA. 2009 Self-organization without conservation: true or just apparent scale-invariance? J. Stat. Mech. 2009, P09009 (doi:10.1088/1742-5468/2009/09/P09009)
41. Bonachela JA, De Franciscis S, Torres JJ, Muñoz MA. 2010 Self-organization without conservation: are neuronal avalanches generically critical? J. Stat. Mech. Theor. Exp. 2010, P02015 (doi:10.1088/1742-5468/2010/ 02/P02015)
42. Gillespie DT. 1977 Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340-2361. (doi:10.1021/j100540a008)
43. Meisel C. 2009 Self-organized criticality in adaptive neural networks. Diploma thesis, Albert-Ludwigs-Universitat Freiburg, Germany. See http://www.biond.org/system/files/preprint/meisel.pdf.
44. Newman MEJ, Strogatz SH, Watts DJ. 2001 Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118. (doi:10.1103/PhysRevE.64.026118)