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Synchronized firing of FitzHugh–Nagumo neurons by noise
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10.1063/1.1929687
/content/aip/journal/chaos/15/2/10.1063/1.1929687
http://aip.metastore.ingenta.com/content/aip/journal/chaos/15/2/10.1063/1.1929687

Figures

Image of FIG. 1.
FIG. 1.

The parameter region in which synchronous firing is observed. in Eq. (1) . indicates the number of synchronized firing neurons. Circled numbers correspond to the parameter setting for the three cases.

Image of FIG. 2.
FIG. 2.

(thin curves) and the number of neurons with synchronous firing (thick curves) as a function of observed in Eq. (1) for and . (a) . (b) . (c) . After a transient time we calculate them using 40 000 time steps data. and the number of neurons with synchronous firing for noise-free case are 0.12 and 3, respectively. The resolution in is the same for both thick and thin curves. We use the smoothing method in Microsoft EXCEL2000 that is similar to cubic spline interpolation.

Image of FIG. 3.
FIG. 3.

Temporal firing pattern after the transient time ( steps) observed in Eq. (1) for and . (a) and . (b) ( ,19,20) and . (c) ( ,18,19,20) and .

Image of FIG. 4.
FIG. 4.

Temporal firing pattern observed in Eq. (1) for and . (a) . (b) ( ,19,20) and .

Image of FIG. 5.
FIG. 5.

and the number of neurons with synchronous firing as a function of observed in Eq. (1) for and . (a) . (b) . and the number of neurons with synchronous firing for noise-free case are 0.01 and 0, respectively.

Image of FIG. 6.
FIG. 6.

Temporal firing pattern observed in Eq. (1) for and . (a) . (b) ( ,19,20) and .

Image of FIG. 7.
FIG. 7.

Two-parameter bifurcation diagram. (solid curve) and (dotted curve) indicate a tangent bifurcation set of five-periodic points and a pitchfork bifurcation set of three-periodic points, respectively. At the closed circle we observe chaotic spikes as shown in Fig. 6(a) .

Image of FIG. 8.
FIG. 8.

One-parameter bifurcation diagram along the lines (a) and (c) in Fig. 7 . (a) . (b) Enlarged diagram of a part of (a). (c) .

Image of FIG. 9.
FIG. 9.

and the number of neurons with synchronous firing as a function of observed in Eq. (1) for and . (a) . (b) . and the number of neurons with synchronous firing for noise-free case are 0.4 and 5, respectively.

Tables

Generic image for table
Table I.

Linear cross correlation between the number of synchronized neurons and first and second the entropy rate.

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/content/aip/journal/chaos/15/2/10.1063/1.1929687
2005-06-07
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Synchronized firing of FitzHugh–Nagumo neurons by noise
http://aip.metastore.ingenta.com/content/aip/journal/chaos/15/2/10.1063/1.1929687
10.1063/1.1929687
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