Bo Deng University of Nebraska-Lincoln Sept. 2004.

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Presentation transcript:

Bo Deng University of Nebraska-Lincoln Sept. 2004

Rinzel & Wang (1997)

Gated Currents by Electrodiffission Ionic Pumps by Chemical Energy

Circuit Model Kandel, E.R., J.H. Schwartz, and T.M. Jessell Principles of Neural Science, 3rd ed., Elsevier, Zigmond, M.J., F.E. Bloom, S.C. Landis, J.L. Roberts, and L.R. Squire Fundamental Neuroscience, Academic Press, Kandel, E.R., J.H. Schwartz, and T.M. Jessell Principles of Neural Science, 3rd ed., Elsevier, Zigmond, M.J., F.E. Bloom, S.C. Landis, J.L. Roberts, and L.R. Squire Fundamental Neuroscience, Academic Press, 1999.

Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(1952), pp Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(1952), pp Alan Lloyd HodgkinAndrew Fielding Huxley

Kirchhoff Laws - I (t)

Mahowald, M. and Douglas, R. A silicon neuron. Nature, 354(1991), pp

Electrophysiological Model Electrophysiological Model Equivalent Circuit Equivalent Circuit Chua, L.O., Introduction to Nonlinear Circuit Theory, McGraw-Hill, New York, 1969.

van der Pol Oscillator (R = 0) and FitzHugh-Nagumo Oscillator van der Pol Oscillator (R = 0) and FitzHugh-Nagumo Oscillator van der Pol (1928), FitzHugh(1961), Nagumo(1964) Keener(1982) van der Pol (1928), FitzHugh(1961), Nagumo(1964) Keener(1982) Balthazar van der Pol ( )

V ILIL I

Morris, C. and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical J., 35(1981), pp Hindmarsh, J.L. and R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Soc. Lond. B. 221(1984), pp Chay, T.R., Y.S. Fan, and Y.S. Lee Bursting, spiking, chaos, fractals, and universality in biological rhythms, Int. J. Bif. & Chaos, 5(1995), pp Izhikevich, E.M Neural excitability, spiking, and bursting, Int. J. Bif. & Chaos, 10(2000), pp (also see his article in SIAM Review) (Non-circuit) Models for Square Burster and Other Bursters Deng(1991)

Disclaimer: With the exception of the square burster and SEED simulation, all artworks are found from the internet.