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), 08 ara fixad FN modal naramatora ond 0.08 b -0.7 and
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), 08 ara fixad FN modal naramatora ond 0.08 b -0.7 and
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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please include matlab code in answer
![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),
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
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
L
- PLOT USE MATLAB
- R=
dv
dI
FEEDBACK LOOP
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 I
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 Ita = 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".
WHEN R<O
AV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae78743c-2e5d-4f29-afad-9b0649e30c33%2F36fa05a9-80fd-42d5-bca6-dace653cf4a5%2Fqmud27_processed.png&w=3840&q=75)
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),
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
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
L
- PLOT USE MATLAB
- R=
dv
dI
FEEDBACK LOOP
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 I
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 Ita = 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".
WHEN R<O
AV
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