Abstract
We propose a method (algorithm) for calculation of the explicit formulas for evolution of the main and the residual overlaps. It allows us to confirm the Gardner-Derrida-Mottishaw second-step formula for the main overlap and to go beyond to the next steps. We discuss the dynamical status of the Amit-Gutfreund-Sompolinsky formula for the main overlap and some computersimulation results.
Similar content being viewed by others
References
W. A. Little,Math. Biosci. 19:101 (1974).
J. J. Hopfield,Proc. Natl. Acad. Sci. USA 79:2554 (1982).
Ch. M. Newman,Neural Networks 1:223 (1988).
V. A. Zagrebnov and A. S. Chvyrov,Sov. Phys.-JETP 68:153 (1989).
A. E. Patrick and V. A. Zagrebnov, A probabilistic approach to parallel dynamics for the Little-Hopfield model,J. Phys. A (submitted).
E. Domany, R. Mair, and W. Kinzel,Europhys. Lett. 2:175 (1986).
A. E. Patrick and V. A. Zagrebnov,J. Phys. France 51:1129 (1990).
E. Domany, R. Meir, and W. Kinzel,J. Phys. A: Math. Gen. 22:2081 (1989).
D. J. Amit, H. Gutfreund, and H. Sompolinsky,Ann. Phys. (NY)173:30 (1987).
A. N. Shiryayev,Probability (Springer-Verlag, New York, 1984).
W. Kinzel,Z. Phys. B 60:205 (1985).
E. Gardner, B. Derrida, and P. Mottishaw,J. Phys. France 48:741 (1987).
A. D. Bruce, E. J. Gardner, and D. J. Wallace,J. Phys. A: Math. Gen. 20:2909 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Patrick, A.E., Zagrebnov, V.A. On the parallel dynamics for the Little-Hopfield model. J Stat Phys 63, 59–71 (1991). https://doi.org/10.1007/BF01026592
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01026592