Abstract
Using a probabilistic approach, the deterministic and the stochastic parallel dynamics of aQ-Ising neural network are studied at finiteQ and in the limitQ→∞. Exact evolution equations are presented for the first time-step. These formulas constitute recursion relations for the parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis of the retrieval properties is carried out in terms of the gain parameter, the loading capacity, and the temperature. The results for theQ→∞ network are compared with those for theQ=3 andQ=4 models. Possible chaotic microscopic behavior is studied using the time evolution of the distance between two network configurations. For arbitrary finiteQ the retrieval regime is always chaotic. In the limitQ→∞ the network exhibits a dynamical transition toward chaos.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Bollé, B. Vinck, and V. A. Zagrebnov,J. Stat. Phys. 70:1099 (1993).
H. Rieger, inStatistical Mechanics of Neural Networks, L. Garrido, ed. (Springer, Berlin, 1990), p. 33.
S. Mertens,J. Phys. A 24:337 (1991).
D. Gandolfo, J. Ruiz, and V. A. Zagrebnov, On the parallel dynamics of the diluted clock neural network, Preprint Marseille CPT-92/P.2728.
J. Jedrzejewski and A. Komoda,Europhys. Lett. 18:275 (1992).
E. Gardner,J. Phys. A 19:L1047 (1986).
C. Newman,Neural Networks 1:223 (1988).
G. M. Zaslavsky, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernikov,Weak Chaos and Quasi-regular Patterns (Cambridge University Press, Cambridge, 1991).
H. Sompolinsky, A. Crisanti, and H. J. Sommers,Phys. Rev. Lett. 61:259 (1988).
B. Tirozzi and M. Tsodyks,Europhys. Lett. 14:727 (1991).
L. Molgedey, J. Schuchardt, and H. G. Schuster,Phys. Rev. Lett. 26:3717 (1992).
M. Bauer and W. Martienssen,J. Phys. A 24:4557 (1991).
B. Derrida, E. Gardner, and A. Zippelius,Europhys. Lett. 4:167 (1987).
B. Derrida,J. Phys. A 20:L721 (1987).
B. Derrida and R. Meir,Phys. Rev. A 38:3116 (1988).
A. N. Shiryaev,Probability (Springer-Verlag, Berlin, 1991).
L. Wang and J. Ross,Phys. Rev. A 44:R2259 (1991).
H. Rieger,J. Phys. A 23:L1273 (1990).
R. Kree and A. Zippelius, inModels of Neural Networks, E. Domany, J. L. van Hemmen, and K. Schulten, eds. (Springer-Verlag, Berlin 1991), p. 193.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bollé, D., Shim, G.M., Vinck, B. et al. Retrieval and chaos in extremely dilutedQ-Ising neural networks. J Stat Phys 74, 565–582 (1994). https://doi.org/10.1007/BF02188571
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02188571