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Phase Plane Dynamics of FitzHugh-Nagumo Model of Neuronal Excitation

​
model parameters
ϵ
0.01
γ
0.5
α
0.1
I
app
0.5
v and w ranges
v
left
-0.5
v
right
1.5
w
left
-0.5
w
right
1.5
p
v
w
dv
dt
= 0
dw
dt
= 0
This Demonstration shows the fast–slow dynamics of the FitzHugh–Nagumo model of neuronal excitation. The main window shows the trajectory in the phase plane of the fast excitation variable
v
and the slow recovery variable
w
, together with the corresponding nullclines.
The smaller graphic on the left shows the time evolution of
v
and
w
.

Details

The traditional FitzHugh–Nagumo equations[1] are
ϵ
dv
dt
=f(v)-w+
I
app
dw
dt
=v-γw
where
f(v)=v(1-v)(v-α)
, for
0<α<1
,
ϵ≪1
.
I
app
is the applied current. Typical values would be
α=0.1
,
γ=0.5
and
ϵ=0.01
.

References

[1] J. P. Keener and J. Sneyd, Mathematical Physiology, 2nd ed., New York: Springer, 2009.

Permanent Citation

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