Cogprints

Order-disorder transition in the Chialvo-Bak `minibrain' controlled by network geometry

Wakeling, Joseph (2003) Order-disorder transition in the Chialvo-Bak `minibrain' controlled by network geometry. [Preprint]

Full text available as:

[img]
Preview
 PDF
212Kb
[img]
Preview
 Postscript
643Kb

Abstract

We examine a simple biologically-motivated neural network, the three-layer version of the Chialvo-Bak `minibrain' [Neurosci. 90 (1999) 1137], and present numerical results which indicate that a non-equilibrium phase transition between ordered and disordered phases occurs subject to the tuning of a control parameter. Scale-free behaviour is observed at the critical point. Notably, the transition here is due solely to network geometry and not any noise factor. The phase of the network is thus a design parameter which can be tuned. The phases are determined by differing levels of interference between active paths in the network and the consequent accidental destruction of good paths.

Item Type:Preprint
Additional Information:Published in Physica A 325 (2003) 561-569.
Keywords:Phase transitions; Neural networks; Neuroscience
Subjects:Neuroscience > Neural Modelling
Computer Science > Neural Nets
ID Code:3152
Deposited By: Wakeling, Joseph
Deposited On:19 Sep 2003
Last Modified:11 Mar 2011 08:55

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

[1] S. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford, 1993.

[2] E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning Ways For Your Mathematical Plays, A. K. Peters, Ltd., 2001.

[3] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59 (1987) 381.

[4] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. A 38 (1998) 364.

[5] P. Bak, K. Sneppen, Phys. Rev. Lett. 71 (1993) 4083.

[6] P. Bak, How Nature Works: The Science of Self-Organized Criticality, Oxford University Press, Oxford, 1997.

[7] D. O. Hebb, The Organization of Behaviour, Wiley, New York, 1949.

[8] A. G. Barto, Hum. Neurobiol. 4 (1985) 229.

[9] A. G. Barto, M. I. Jordan, Proc. IEEE Int. Conf. on Neural Networks 2 (1987) 629.

[10] P. Mazzoni, R. A. Andersen, M. I. Jordan, Proc. Natl. Acad. Sci. USA 88 (1991) 4433.

[11] P. Alstrom, D. Stassinopoulos, Phys. Rev. E 51 (1995) 5027.

[12] D. Stassinopoulos, P. Bak, Phys. Rev. E 51 (1995) 5033.

[13] D. R. Chialvo, P. Bak, Neurosci. 90 (1999) 1137.

[14] P. Bak, D. R. Chialvo, Phys. Rev. E 63 (2001) 031912.

[15] J. Wakeling, P. Bak, Phys. Rev. E 64 (2001) 051920.

[16] T. Kohonen, Self-Organizing Maps, Springer-Verlag, Berlin, 2001.

[17] J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79 (1982) 2554.

[18] D. J. Amit, H. Gutfreund, H. Sompolinsky, Phys. Rev. Lett. 55 (1985) 1530.

[19] E. Gardner, J. Phys. A 20 (1987) 3453.

[20] H. Sompolinsky, N. Tishby, H. S. Seung, Phys. Rev. Lett. 65 (1990) 1683.

[21] E. Barkai, D. Hansel, H. Sompolinsky, Phys. Rev. A 45 (1992) 4146.

[22] H. S. Seung, H. Sompolinsky, N. Tishby, Phys. Rev. A 45 (1992) 6056.

[23] T. L. H. Watkin, A. Rau, M. Biehl, Rev. Mod. Phys. 65 (1993) 499.

[24] J. A. Flanagan, Phys. Rev. E 63 (2001) 036130.

[25] G. Parisi, J. Phys. A 19 (1986) L617.

[26] J. Z. Young, Proc. Royal Soc. London B 163 (1965) 285.

[27] R. M. Fitzsimonds, H. J. Song, M. M. Poo, Nature 388 (1997) 439.

[28] J. S. Albus, Brains, Behaviour and Robotics, BYTE Books, McGraw-Hill, Peterborough, NH, 1981.

[29] G. M. Edelman, Neural Darwinism: The Theory of Neuronal Group Selection, Basic Books, New York, 1987.

[30] T. Araujo, R. Vilela Mendes, Complex Syst. 12 (2000) 357.

Metadata

Repository Staff Only: item control page

Cogprints is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.