Limit cycles of a perceptron

An artificial neural network can be used to generate a series of numbers. A Boolean perceptron generates bit sequences with a periodic structure. The corresponding spectrum of cycle lengths is investigated analytically and numerically; it has similarities with properties of rational numbers.

[1]  E. Caianiello.  Outline of a theory of thought-processes and thinking machines. , 1961, Journal of theoretical biology.

[2]  Eric Goles Ch.,et al.  Dynamical Behavior of a Neural Automaton with Memory , 1988, Complex Syst..

[3]  Eric Goles Ch.,et al.  Bifurcation structure of a discrete neuronal equation , 1988, Discret. Appl. Math..

[4]  W. Kinzel.  Physics of Neural Networks , 1990 .

[5]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[6]  T. Watkin,et al.  THE STATISTICAL-MECHANICS OF LEARNING A RULE , 1993 .

[7]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[8]  Kanter,et al.  Generation and prediction of time series by a neural network. , 1995, Physical review letters.

[9]  Kanter,et al.  Analytical study of time series generation by feed-forward networks. , 1995, Physical review letters.

[10]  I. Kanter,et al.  Training a perceptron by a bit sequence: storage capacity , 1996 .

[11]  Mike Mannion,et al.  Complex systems , 1997, Proceedings International Conference and Workshop on Engineering of Computer-Based Systems.