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Temperature-dependent stochastic dynamics of the Huber-Braun neuron model
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10.1063/1.3668044
/content/aip/journal/chaos/21/4/10.1063/1.3668044
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3668044
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Attractor bifurcation diagrams of interspike intervals vs. temperature. The ISIs correspond to the Poincaré return time for a surface of section at V = −20 mV. (a) The deterministic scenario; (b) Gaussian white noise of intensity D = 0.5 is implemented only in the voltage variable V; (c) Gaussian white noise of intensity D = 0.00002 is implemented only in the slow repolarizing variable ; (d) Gaussian white noise of intensity D = 0.00002 added to both activation variables ar and asd . We use different noise realizations in every variable. To help the eye, the parametric locus of the deterministic homoclinic bifurcation is indicated by a vertical arrow in each panel.

Image of FIG. 2.
FIG. 2.

Deterministic time series of the membrane voltage at different temperature values. (a) Tonic firing at T = 4 °C; (b) Chaotic bursting below the homoclinic bifurcation at T = 10 °C; (c) Chaotic bursting beyond the homoclinic bifurcation at T = 11.5 °C; and (d) Period-2 bursting at T = 25 °C. The homoclinic bifurcation is located at T = 10.7 °C. In panels (b)–(d), subthreshold oscillations are clearly visible.

Image of FIG. 3.
FIG. 3.

State space dynamics of the Huber-Braun model at (a) T = 4 °C (deterministic period-one solution) and (b) T = 25 °C (deterministic period-two solution). The deterministic solutions are shown as a solid black line, the grey trajectories show the situation when the voltage variable V is subjected to additive Gaussian white noise of intensity D = 0.5. The circle indicates the position of the saddle equilibrium. The corresponding voltage traces are depicted in Figs. 6(a) and 6(b).

Image of FIG. 4.
FIG. 4.

State space dynamics of the Huber-Braun model at (a) T = 4 °C (deterministic period-one solution) and (b) T = 25 °C (deterministic period-two solution). The deterministic solutions are shown as a solid black line, the grey trajectories show the situation when the slow repolarizing variable is subjected to additive Gaussian white noise of intensity D = 0.00002. The circle indicates the position of the saddle equilibrium. The corresponding voltage traces are depicted in Figs. 6(c) and 6(d).

Image of FIG. 5.
FIG. 5.

State space dynamics of the Huber-Braun model at T = 10 °C. The position of the saddle, indicated by a circle, is shown in relation to the noisy attractor of the system when it is subjected to Gaussian white noise of intensity D = 0.00002 in . In this parameter regime close to the homoclinic bifurcation, the effects of current or conductance noise do not differ substantially from the deterministic scenario and practically lead to the same attractor structure.

Image of FIG. 6.
FIG. 6.

Noisy time series of the membrane voltage at different temperature values, corresponding to the state space diagrams in Figs. 3 and 4. (a) Current noise of intensity D = 0.5 at T = 4 °C and (b) at T = 25 °C (cf. Fig. 3); (c) Conductance noise of intensity D = 0.00002 at T = 4 °C and (d) at T = 25 °C (cf. Fig. 4).

Image of FIG. 7.
FIG. 7.

Histogram plots showing the number of interspike intervals on a logarithmic scale versus the interspike intervals (a) at T = 10 °C and T = 11.5 °C, (b) at T = 8 °C and T = 25 °C, and (c) at T = 4 °C and T = 30 °C for conductance noise in of intensity D = 0.00002. The temperature values have been chosen in a way that the deterministic system is in a chaotic mode before and after the homoclinic bifurcation in panel (a) and in a tonic firing mode before and after the homoclinic bifurcation in panel (c). The statistics have been taken for 20 000 interspike intervals and a bin width of 0.02.

Image of FIG. 8.
FIG. 8.

The distribution of interspike intervals at T = 10 °C and T = 11.5 °C in the deterministic system.

Image of FIG. 9.
FIG. 9.

The data points of the exponentially decaying flank of interspike intervals at T = 4 °C (cf. Fig. 7(c)) together with the exponential fit (solid line).

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/content/aip/journal/chaos/21/4/10.1063/1.3668044
2011-12-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Temperature-dependent stochastic dynamics of the Huber-Braun neuron model
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3668044
10.1063/1.3668044
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