Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit

Yasutomo OHGUCHI; Yukio YANO; Kenzo MURAZUMI

Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit

Yasutomo OHGUCHI, Yukio YANO, Kenzo MURAZUMI

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Responses in the Nagumo neural circuit to pulse-train stimulation are studied using the time sequence, phase diagram, Poincare section, return map, firing rate, Lyapunov number and bifurcation diagram. For the mono-stable neuron with an equilibrium point deeper than the maximal point of a tunnel diode curve, main responses are periodic or all-or-none and chaotic responses are rarely observed. For the neuron with an equilibrium point located near the maximal point, the response to one input pulse oscillates after the undershoot and responses to pulse-trains make complex bifurcation structure in the threshold diagram. The ranges of periodic responses are stratified in the diagram. There exist broad regions of chaotic responses and chaos is not a special response of the Nagumo circuit, but it often comes out. The results are different from those obtained from Hodgkin-Huxley equations and the BVP model.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.3 pp.459-466

Publication Date: 1993/03/25

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Type of Manuscript: PAPER

Category: Nonlinear Phenomena and Analysis

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Yasutomo OHGUCHI, Yukio YANO, Kenzo MURAZUMI, "Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 3, pp. 459-466, March 1993, doi: .
Abstract: Responses in the Nagumo neural circuit to pulse-train stimulation are studied using the time sequence, phase diagram, Poincare section, return map, firing rate, Lyapunov number and bifurcation diagram. For the mono-stable neuron with an equilibrium point deeper than the maximal point of a tunnel diode curve, main responses are periodic or all-or-none and chaotic responses are rarely observed. For the neuron with an equilibrium point located near the maximal point, the response to one input pulse oscillates after the undershoot and responses to pulse-trains make complex bifurcation structure in the threshold diagram. The ranges of periodic responses are stratified in the diagram. There exist broad regions of chaotic responses and chaos is not a special response of the Nagumo circuit, but it often comes out. The results are different from those obtained from Hodgkin-Huxley equations and the BVP model.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e76-a_3_459/_p

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@ARTICLE{e76-a_3_459,
author={Yasutomo OHGUCHI, Yukio YANO, Kenzo MURAZUMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit},
year={1993},
volume={E76-A},
number={3},
pages={459-466},
abstract={Responses in the Nagumo neural circuit to pulse-train stimulation are studied using the time sequence, phase diagram, Poincare section, return map, firing rate, Lyapunov number and bifurcation diagram. For the mono-stable neuron with an equilibrium point deeper than the maximal point of a tunnel diode curve, main responses are periodic or all-or-none and chaotic responses are rarely observed. For the neuron with an equilibrium point located near the maximal point, the response to one input pulse oscillates after the undershoot and responses to pulse-trains make complex bifurcation structure in the threshold diagram. The ranges of periodic responses are stratified in the diagram. There exist broad regions of chaotic responses and chaos is not a special response of the Nagumo circuit, but it often comes out. The results are different from those obtained from Hodgkin-Huxley equations and the BVP model.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 459
EP - 466
AU - Yasutomo OHGUCHI
AU - Yukio YANO
AU - Kenzo MURAZUMI
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1993
AB - Responses in the Nagumo neural circuit to pulse-train stimulation are studied using the time sequence, phase diagram, Poincare section, return map, firing rate, Lyapunov number and bifurcation diagram. For the mono-stable neuron with an equilibrium point deeper than the maximal point of a tunnel diode curve, main responses are periodic or all-or-none and chaotic responses are rarely observed. For the neuron with an equilibrium point located near the maximal point, the response to one input pulse oscillates after the undershoot and responses to pulse-trains make complex bifurcation structure in the threshold diagram. The ranges of periodic responses are stratified in the diagram. There exist broad regions of chaotic responses and chaos is not a special response of the Nagumo circuit, but it often comes out. The results are different from those obtained from Hodgkin-Huxley equations and the BVP model.
ER -