FitzHugh-Naguno Neuron. The FitzHugh-Naguno (FN) model is a simplified mathematical model of spiking neuronal dynamics of the giant squid axon, given by the following set of coupled differential equations: dV dt dW dt = ƒ(V) — W+I = a(V+b−cW) where V is the neuron membrane potential (accounting for sodium-mediated excitation), W is the accommodation variable (accounting for potasium-mediated refraction), I is the current injected into the neuron, ƒ(V) = V - V³/3 is a nonlinear activation function (modeling sodium excitability), and a = 0.08, b= 0.7 and c = 0.8 are fixed FN model parameters. The purpose is to instantiate the above dynamics of the FN model using a rcuit driven by an external current I, and producing the voltage V and the current W as shown in e circuit diagram below. The tunnel diode in the circuit diagram is a type of nonlinear resistor, i.e., carries a current Itd that is a nonlinear function of the voltage V across it. tunnel diode R E Write down the set of ordinary differential equations describing the dynamics of the above electronic circuit in voltage V and current W, for a given input current I. You may assume the tunnel diode has a current-voltage characteristic given by Itd = g(V). Now identify the functional form Itd = g(V) for the current-voltage characteristic of the tunnel diode, and values for the capacitance C, resistance R, and inductance L, in order to align the dynamics of the circuit with that of the FN model, for given nonlinearity ƒ(V) and given parameters a, b, and c in the FN model. Plot the tunnel diode current-voltage characteristic Itd = g(V), i.e., the current through the tunnel diode Itd as a function of the membrane voltage V across it. Identify the voltage re- gion over which the tunnel diode has negative resistance, i.e., where the current decreases with increasing voltage. Explain the role of this negative resistance in making the circuit "spike".
FitzHugh-Naguno Neuron. The FitzHugh-Naguno (FN) model is a simplified mathematical model of spiking neuronal dynamics of the giant squid axon, given by the following set of coupled differential equations: dV dt dW dt = ƒ(V) — W+I = a(V+b−cW) where V is the neuron membrane potential (accounting for sodium-mediated excitation), W is the accommodation variable (accounting for potasium-mediated refraction), I is the current injected into the neuron, ƒ(V) = V - V³/3 is a nonlinear activation function (modeling sodium excitability), and a = 0.08, b= 0.7 and c = 0.8 are fixed FN model parameters. The purpose is to instantiate the above dynamics of the FN model using a rcuit driven by an external current I, and producing the voltage V and the current W as shown in e circuit diagram below. The tunnel diode in the circuit diagram is a type of nonlinear resistor, i.e., carries a current Itd that is a nonlinear function of the voltage V across it. tunnel diode R E Write down the set of ordinary differential equations describing the dynamics of the above electronic circuit in voltage V and current W, for a given input current I. You may assume the tunnel diode has a current-voltage characteristic given by Itd = g(V). Now identify the functional form Itd = g(V) for the current-voltage characteristic of the tunnel diode, and values for the capacitance C, resistance R, and inductance L, in order to align the dynamics of the circuit with that of the FN model, for given nonlinearity ƒ(V) and given parameters a, b, and c in the FN model. Plot the tunnel diode current-voltage characteristic Itd = g(V), i.e., the current through the tunnel diode Itd as a function of the membrane voltage V across it. Identify the voltage re- gion over which the tunnel diode has negative resistance, i.e., where the current decreases with increasing voltage. Explain the role of this negative resistance in making the circuit "spike".
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:FitzHugh-Naguno Neuron. The FitzHugh-Naguno (FN) model is a
simplified mathematical model of spiking neuronal dynamics of the giant squid axon, given by the
following set of coupled differential equations:
dV
dt
dW
dt
= f(V) − W + I
= a (V+b-cW)
where V is the neuron membrane potential (accounting for sodium-mediated excitation), W is the
accommodation variable (accounting for potasium-mediated refraction), I is the current injected into
the neuron, f(V) = V - V³/3 is a nonlinear activation function (modeling sodium excitability),
0.08, b = 0.7 and c = 0.8 are fixed FN model parameters.
and a =
The purpose is to instantiate the above dynamics of the FN model using a
ircuit driven by an external current I, and producing the voltage V and the current W as shown in
he circuit diagram below. The tunnel diode in the circuit diagram is a type of nonlinear resistor, i.e.,
t carries a current Itd that is a nonlinear function of the voltage V across it.
tunnel
diode
R
E
Write down the set of ordinary differential equations describing the dynamics of
the above electronic circuit in voltage V and current W, for a given input current I. You may
assume the tunnel diode has a current-voltage characteristic given by Itd = g(V).
Now identify the functional form Itd = g(V) for the current-voltage characteristic of
the tunnel diode, and values for the capacitance C, resistance R, and inductance L, in order to
align the dynamics of the circuit with that of the FN model, for given nonlinearity f(V) and
given parameters a, b, and c in the FN model.
Plot the tunnel diode current-voltage characteristic Itd = g(V), i.e., the current through
the tunnel diode Itd as a function of the membrane voltage V across it. Identify the voltage re-
gion over which the tunnel diode has negative resistance, i.e., where the current decreases with
increasing voltage. Explain the role of this negative resistance in making the circuit "spike".
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