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1
φ
1
3
S
0.5
2
80 100
t
1
20
40
60
0.5
1
f
1
0.2 0.4 0.6 0.8
1
φ
S
1
3
0.5
2
80 100
t
1
20
40
60
0.5
1
f
1
0.2 0.4 0.6 0.8
1
φ
1
3
S
0.5
2
00
t
1
20
40
60
80
0.5
1
f
1
0.2 0.4 0.6 0.8
Figure 3.27. The dynamics of the FitzHugh-Nagumo system (
3.66
) and (
3.67
)for
different noise amplitudes (
a
=
1
.
05,
=
0
.
01).
s
gn
=
0
.
02,
s
gn
=
0
.
07, and
s
gn
=
0
25, from top to bottom, respectively. The panels in the left column report the time
series, the panels in the right column the corresponding power spectra.
.
a random modulation of the bifurcation parameter
a
. However, this modulation is not
essential for the occurrence of stochastic coherence. In fact, this behavior emerges
even if the noise component is moved from Eq. (
3.66
)toEq.(
3.67
).
Apart from the details related to this specific model, the key point of stochastic
coherence is that noise can cooperate with an intrinsic time scale of the deterministic
dynamics (
t
e
in the FitzHugh-Nagumo model) to induce regular oscillatory behavior.
In this sense, noise is able to unveil a time scale that would be hidden in a deterministic
dynamics. In fact, in the absence of noise
φ
(
t
) would just tend to a point attractor
(
Sagues et al.
,
2007
).
3.5 Noise-induced net transport
One of the most counterintuitive noise-induced phenomena investigated in the past
few decades is associated with the ability of unbiased random fluctuations to generate
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