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Noise effects in an electronic model of a single neuron


We consider a simple electronic circuit model of a single neuron. The neuron is assumed to be driven by an external signal comprising constant (dc) and random components. In addition, the nonlinearity parameter in the circuit is assumed to fluctuate, thereby giving rise to critical behavior including the onset of hysteresis phenomena even for system parameter values that would not otherwise support such behavior. This “noise-induced critical behavior” is analysed, in the long time limit, through a study of the probability density function describing the neural response.

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  1. Babcock KL, Westervelt R (1986) Stability and dynamics of simple electronic neural networks with added inertia. Physica 23D:464–469

  2. Babcock KL, Westervelt R (1987) Dynamics of simple elctronic neural networks. Physica 28D:305–316

  3. Budgor AB, Lindenberg K, Shuler K (1976) Studies in nonlinear stochastic processes. II. The Duffing oscillator revisited. J Stat Phys 15:375–391

  4. Buhmann J, Shulten K (1986) Influence of noise on the behavior of an autoassociative neural network. In: Denker J (eds) Neural networks for computing. AIP Conference Proceedings, vol 151. AIP 1986

  5. Buhmann J, Shulten K (1987) Influence of noise on the function of a “physiological” neural network. Biol Cybern 56:313–327

  6. Bulsara AR, Schieve W, Gragg R (1978) Phase transitions induced by white noise in bistable optical systems. Phys Lett 68A:294–296

  7. Bulsara AR, Lindenberg K, Seshadri S, Shuler K, West B (1979) Stochastic processes with non-additive fluctuations. II. Some applications of the Ito and Stratonovich calculus. Physica 97A:234–243

  8. Bulsara AR, Lindenberg K, Shuler K, Frelich R, Coles W (1982a) Analog computer simulation of a Duffing oscillator and comparison with statistical linearization. Int J Non-Lin Mech 17:237–253

  9. Bulsara AR, Lindenberg K, Shuler K (1982b) Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory. J Stat Phys 27:787–808

  10. Bulsara AR, Schieve W, Jacobs E (1987) Noise-induced critical behavior in a multistable system. Physica 146A:126–150

  11. Chandrasekhar S (1943) Stochastic problems in physics and astronomy. Rev Mod Phys 15:1–91

  12. Englund JC, Snapp R, Schieve W (1984) Fluctuations, instabilities and chaos in the laserdriven nonlinear ring cavity. In: Wolf E (ed) Progress in optics, vol XXI. North-Holland, Amsterdam

  13. Gardiner CW (1984) Handbook of stochastic processes. Springer, Berlin Heidelberg New York

  14. Goel NS, Richter-Dyn N (1974) Stochastic models in biology. Academic Press, New York

  15. Haken H (1977) Synergetics. Springer, Berlin Heidelberg New York

  16. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554–2558

  17. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092

  18. Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer, Berlin Heidelberg New York

  19. Kampen N van (1985) Stochastic processes in physics and chemistry. North-Holland, Amsterdam

  20. Lindenberg K, Seshadri V (1981) Dissipative contributions of internal multiplicative noise. I. Mechanical oscillator. Physica 109A:483–499

  21. Mannella R, Faetti S, Grigolini P, McClintock P, Moss F (1986) The effect of multiplicative noise on the relaxation time of a real non-linear physical system: a comparison of experiment and theory for the random growing rate model (RGRM). J Phys. A 19:L699-L704

  22. Moss F, McClintock P (1984) Experimental studies of noise-induced transitions. In: Horsthemke W, Kondepudi D (eds) Fluctuations and sensitivity in nonequilibrium systems. Springer, Berlin Heidelberg New York

  23. Oppenheim I, Shuler K, Weiss G (1977) Stochastic processes in chemical physics — the master equation. MIT Press, Cambridge, Mass

  24. Risken R (1984) The Fokker Planck equation. Springer, Berlin Heidelberg New York

  25. Schenzle A, Brand H (1979) Multiplicative stochastic processes in statistical physics. Phys Rev A 20:1628–1647

  26. Wang M, Uhlenbeck G (1945) Theory of the Brownian motion. Rev Mod Phys 17:323–342

  27. West B, Bulsara A, Lindenberg K, Seshadri V, Shuler K (1979) Stochastic processes with non-additive fluctuations I. Ito and Stratonovich calculus and the effects of correlations. Physica 97A:211–233

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Bulsara, A.R., Boss, R.D. & Jacobs, E.W. Noise effects in an electronic model of a single neuron. Biol. Cybern. 61, 211–222 (1989).

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  • Density Function
  • Probability Density
  • Time Limit
  • Probability Density Function
  • System Parameter