- Access by Xinjiang University
Generation of unpredictable time series by a neural network
Phys. Rev. E 63, 056126 – Published 26 April, 2001
DOI: https://doi.org/10.1103/PhysRevE.63.056126
Abstract
A perceptron that “learns” the opposite of its own output is used to generate a time series. We analyze properties of the weight vector and the generated sequence, such as the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model are discussed. If a continuous transfer function is used, the system displays chaotic and intermittent behavior, with the product of the learning rate and amplification as a control parameter.
References (26)
- H. Zhu and W. Kinzel, Neural Comput. 10, 2219 (1998).
- J. Hertz, A. Krogh, and R. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Redwood City, CA, 1991).
- E. Eisenstein, I. Kanter, D. A. Kessler, and W. Kinzel, Phys. Rev. Lett. 74, 6 (1995).
- M. Schröder, Ph.D. thesis, Universität Würzburg, 1998.
- M. Schröder and W. Kinzel, J. Phys. A 31, 9131 (1998).
- On-Line Learning in Neural Networks, edited by D. Saad (Cambridge University Press, Cambridge, 1998).
- G. Reents and R. Urbanczik, Phys. Rev. Lett. 80, 5445 (1998).
- S. Mertens and C. Bessenrodt, J. Phys. A 31, 3731 (1998).
- M. Schroeder, Number Theory in Science and Communication (Springer-Verlag, Berlin, 1984).
- J. Bernasconi, J. Phys. (France) 48, 559 (1987).
- M. J. E. Golay, IEEE Trans. Inf. Theory IT-28, 543 (1982).
- C. de Groot, D. Würtz, and K. H. Hoffmann, Optimization23, 369 (1992).
- S. Mertens, J. Phys. A 29, L473 (1996).
- http://itp.nat.uni-magdeburg.de/ ̃|P5;mertens/bernasconi/cyclic.shtml
- C. Van den Broeck and R. Kawai, Phys. Rev. A 42, 6210 (1990).
- I. Kanter and D. A. Kessler, Phys. Rev. Lett. 74, 4559 (1995).
- D. Challet and M. Marsili, e-print, cond-mat/0004196.
- I. Kanter, D. A. Kessler, A. Priel, and E. Eisenstein, Phys. Rev. Lett. 75, 2614 (1995).
- A. Priel, I. Kanter, and D. A. Kessler, J. Phys. A 31, 1189 (1998).
- A. Priel and I. Kanter, Phys. Rev. E 59, 3368 (1999).
- I. Kanter, Phys. Rev. A 38, 5972 (1988).
- I. Kanter and D. Saad, Phys. Rev. Lett. 83, 2660 (1999).
- E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
- Introduction to Nonlinear Physics, edited by L. Lam (Springer, New York, 1997).
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Physica D 16, 285 (1985).
- J. Kaplan and J. Yorke, in Functional Differential Equations and Approximations of Fixed Points, edited by H. Peitgen and H. Walther (Springer, Heidelberg, 1979).