Guckenheimer, J., Gueron, S., and Harris-Warrick, R. M. The dynamics of a conditionally bursting neuron. (submitted). Guckenheimer, J. and Holmes, P. 1983. Nonlinear Oscillation, Dynamical Dystems, and Bifurcations of Vector Fields. Springer-Verlag, New York, NY. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Dimension Reduction of Biological Neuron Models by.. - Doya, Selverston (1994) (6 citations) (Correct)
....i can be assigned a distinct time constant i so that events on the time scale near i will be represented primarily by unit i. Furthermore, the time constants can be fine tuned by the learning algorithm described below. In general, the dynamics of a recurrent network can go through bifurcations (Guckenheimer and Holmes 1983) in the course of learning. In such cases, the output error of the network can be increased abruptly by gradient descent algorithms and the learning equations can be numerically unstable (Doya 1992) Because the recurrence of our network is limited to 3 the local linear feedback in teacher ....
Guckenheimer, J., Gueron, S., and Harris-Warrick, R. M. The dynamics of a conditionally bursting neuron. (submitted). Guckenheimer, J. and Holmes, P. 1983. Nonlinear Oscillation, Dynamical Dystems, and Bifurcations of Vector Fields. Springer-Verlag, New York, NY.
Near Saddle-Node Bifurcation Behavior as Dynamics in Working.. - Nakahara, Doya (1998) (6 citations) (Correct)
....of single dynamical systems. Nonlinear dynamical system theory has been successfully applied to modeling neural mechanisms and cognitive systems at different levels (Port and Van Gelder 1995; Kelso 1995) such as the level of single neurons (Rinzel and Ermentrout 1989; Marder and Abbott 1995; Guckenheimer, Gueron, and Harris Warrick 1993), motor behaviors (Taga 1995; Collins and Stewart 1993; Beer 1995) and language (Elman 1995) Techniques of researches in artificial life such as evolutionary programming are helpful in exploring what cognitive functions are necessary for behaving in various environments (Belew and Mitchell ....
Guckenheimer, J., S. Gueron, and R. M. Harris-Warrick (1993). The dynamics of a conditionally bursting neuron. Philosophical Transactions of the Royal Society of London.
Bifurcation of the Hodgkin and Huxley Equations: A New Twist - Guckenheimer, Labouriau (1995) (1 citation) Self-citation (Guckenheimer) (Correct)
....overcome this difficulty for the HodgkinHuxley model of voltage clamped action potentials in squid axons. The use of these methods to make comparisons between experimental data and compartmental models of a conditionally bursting neuron have been pursued by Guckenheimer, Gueron and Harris Warrick [9] Simpler models of action potentials for nerve impulses based upon planar vector fields have been extensively studied. While these models display many aspects of solutions to the Hodgkin Huxley equations [6, 23, 19] some of the features of HH dynamics described here cannot be found in systems of ....
Guckenheimer J, Gueron S, Harris-Warrick RM (1992) The dynamics of conditionally bursting neuron, submitted for publication.
Reduction of a Channel Based Model for a.. - Golomb, Guckenheimer, .. (1993) (1 citation) Self-citation (Guckenheimer Gueron) (Correct)
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Guckenheimer J, Gueron S, Harris-Warrick RM (1992) The dynamics of conditionally bursting neuron, submitted for publication.
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