Advertisement

A new model for simple neural nets and its application in the design of a neural oscillator

  • Theodosios Pavlidis
Article

Abstract

The results of a previous theoretical study of a class of systems are applied for the design of neural nets which try to simulate biological behavior.

Besides the models for single aperiodic and periodic neurons, a “neural oscillator” is developed which consists of two cross-excited neurons. Its response is similar to the firing pattern of certain biological neural oscillators, like the flying system of the locust. Also, by proper change of its parameters, it can be made highly irregular, providing a deterministic model for the spontaneous neural activity.

Keywords

Neural Oscillator Artificial Neuron Pulse Frequency Modulation Approximate System Spontaneous Neural Activity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Literature

  1. Bertaux, D. 1963.Mathematical Model of a Synapse. M.S. Research Project (Plan II), Dept. Electr. Engr., University of California, Berkeley; Sept.Google Scholar
  2. Crane, H. D. 1962. “Neuristor—A Novel Device and System Concept.”IRE Proc.,50, No. 10, 2048–2060.CrossRefGoogle Scholar
  3. Fetz, E. E. and G. L. Gerstein. 1963. “An RC Model for Spontaneous Activity of Single Neurons.”MIT Quarterly Report of the Res. Lab. of Electronics,71, 249–256.Google Scholar
  4. Gardner, M. F. and J. L. Barnes. 1942.Transients in Linear Systems. New York: J. Wiley.zbMATHGoogle Scholar
  5. Gerstein, G. L. and B. Mandelbrot. 1964. “Random Walk Models for the Spike Activity of a Single Neuron.”Biophysical Journal,4, No. 1, pt. 1, 41–68.CrossRefGoogle Scholar
  6. Harmon, L. D. 1961. “Studies with Artificial Neurons, I: Properties and Functions of an Artificial Neuron.”Kybernetik,1, No. 3, 89–101.CrossRefGoogle Scholar
  7. — 1962. “Neural Analogs.”Proc. of the Spring Joint Computer Conference, San Francisco,21, 153–158.Google Scholar
  8. Hiltz, F. F. 1963. “Artificial Neuron.”Kybernetik,1, No. 6, 231–236.Google Scholar
  9. Jury, E. I. and T. Pavlidis. 1963. “A. Literature Survey of Biocontrol Systems.”IEEE Trans. on Automatic Control,8, No. 3, 210–217.CrossRefGoogle Scholar
  10. Kalman, R. E. 1956. “Nonlinear Aspects of Sampled-Data Control Systems.”Proc. of the Symposium on Nonlinear Circuit Analysis, Brooklyn Pol. Inst., 273–313.Google Scholar
  11. Landahl, H. D. 1961. “A Note on Mathematical Models for the Interaction of Neural Elements.”Bull. Math. Biophysics,23, 91–97.CrossRefMathSciNetGoogle Scholar
  12. Lewis, E. R. 1963. “An Electronic Analog of the Neuron Based on the Dynamics of Potassium and Sodium Ion Fluxes.”Semi-Annual Report No. 6, The Lab. for Automata Research, General Precision, Inc., 57–109, Jan.Google Scholar
  13. Li, C. C. 1961.Integral Pulse Frequency Modulated Control Systems. Ph.D. Dissertation, Northwestern University.Google Scholar
  14. Nelson, P. P. 1962. “Un Modele du neurone.”Bull. Math. Biophysics,24, 159–181.zbMATHCrossRefGoogle Scholar
  15. Ormsby, J. F. A. 1962.On the Generation of Markov Chains. Electr. Res. Lab. Report No. 60-480, University of California, Berkeley.Google Scholar
  16. Pavlidis, T. 1963.Neural Pulse Frequency Modulation Control Systems. Int. Tech. Memo, M-15, Electronics Research Lab., University of California, Berkeley.Google Scholar
  17. — 1964.Analysis and Synthesis of Pulse Frequency Modulation Feedback Systems. Ph.D. Dissertation, Dept. of Electrical Engineering, University of California, Berkeley. Also available as an Electronics Research Laboratory Report No. 64-13, March 10, 1964.Google Scholar
  18. Pavlidis, T. and E. I. Jury. 1965.Analysis of a New Class of Pulse-Frequency Modulated Feedback Systems. IEEE Transactions on Automatic Control.Google Scholar
  19. Rashevsky, N. 1960.Mathematical Biophysics, 3rd Edition, Vol. 1, and 2. New York: Dover Publications, Inc.Google Scholar
  20. Ruch, T. C. and J. F. Fulton. 1960.Medical Physiology and Biophysics. Philadelphia: W. B. Saunders.Google Scholar
  21. Wilson, D. M. 1961. “The Central Nervous Control of Flight in a Locust.”Jour. Exper. Biology,38, 888–908.Google Scholar
  22. Wilson, D. M. and T. Weis-Fogh. 1962. “Patterned Activity of Coordinated Motor Units, Studied in Flying Locusts.”Jour. Exper. Physiology,39, 643–667.Google Scholar
  23. Wilson, D. M. and E. Gettrup. 1963. “A Stretch Reflex Controlling Wingbeat Frequency in Grasshoppers.”Jour. Exper. Physiology,40, 171–185.Google Scholar
  24. Zadeh, L. A. and C. A. Desoer. 1963.Linear System Theory—The State Space Approach. New York: McGraw-Hill.zbMATHGoogle Scholar

Copyright information

© N. Rashevsky 1965

Authors and Affiliations

  • Theodosios Pavlidis
    • 1
  1. 1.Department of Electrical EngineeringPrinceton UniversityPrinceton

Personalised recommendations