Find power laws for plots

[jrieke]

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[jrieke]

@borismarin You said that certain power laws indicate certain bifurcations - do you have any literature on that?

[borismarin]

Strogatz table 7.4.1 p 264
On 11 Nov 2015 01:07, "Johannes Rieke" notifications@github.com wrote:

@borismarin https://github.com/borismarin You said that certain power
laws indicate certain bifurcations - do you have any literature on that?

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#8 (comment)
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[jrieke]

See red curves in plots below. Only fitted a small region near the bifurcations (in accordance with Strogatz). Made both curves go through zero at the values of the bifurcations (-2.73 pA and 59.70 pA).

f-I-curve (inverse logarithmic fit near the homoclinic bifurcation; form of the equation is taken from Izhikevich book, fig. 6.30 on p. 189):

Amplitudes (square root fit near the supercritical Hopf):

[borismarin]

Lovely. Maybe it will be clearer if you factor out par-par* where par* is
the parameter value for the bifurcations.
On 19 Dec 2015 03:49, "Johannes Rieke" notifications@github.com wrote:

See red curves in plots below. Only fitted a small region near the
bifurcation (in accordance with Strogatz).

f-I-curve (inverse logarithmic fit near the homoclinic bifurcation; form
of the equation is taken from Izhikevich book, fig. 6.30 on p. 189):

[image: f-i-curve]
https://cloud.githubusercontent.com/assets/5103165/11911101/0c3a114c-a60b-11e5-88df-4daf86eaed9b.png

Amplitudes (square root fit near the supercritical Hopf):

[image: amplitudes]
https://cloud.githubusercontent.com/assets/5103165/11911103/10452a6a-a60b-11e5-9493-79d2083ac8ff.png

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#8 (comment)
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[borismarin]

BTW, do you say "mean firing rate" because firing is irregular or because
you are not disregarding transients?

On 19 December 2015 at 12:34, Bóris Marin borismarin@gmail.com wrote:

Lovely. Maybe it will be clearer if you factor out par-par* where par* is
the parameter value for the bifurcations.
On 19 Dec 2015 03:49, "Johannes Rieke" notifications@github.com wrote:

See red curves in plots below. Only fitted a small region near the
bifurcation (in accordance with Strogatz).

f-I-curve (inverse logarithmic fit near the homoclinic bifurcation; form
of the equation is taken from Izhikevich book, fig. 6.30 on p. 189):

[image: f-i-curve]
https://cloud.githubusercontent.com/assets/5103165/11911101/0c3a114c-a60b-11e5-88df-4daf86eaed9b.png

Amplitudes (square root fit near the supercritical Hopf):

[image: amplitudes]
https://cloud.githubusercontent.com/assets/5103165/11911103/10452a6a-a60b-11e5-9493-79d2083ac8ff.png

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#8 (comment)
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[borismarin]

I'd also have an inset for the f-I plot zooming around 0 pA

On 19 December 2015 at 13:13, Bóris Marin borismarin@gmail.com wrote:

BTW, do you say "mean firing rate" because firing is irregular or because
you are not disregarding transients?

On 19 December 2015 at 12:34, Bóris Marin borismarin@gmail.com wrote:

Lovely. Maybe it will be clearer if you factor out par-par* where par* is
the parameter value for the bifurcations.
On 19 Dec 2015 03:49, "Johannes Rieke" notifications@github.com wrote:

See red curves in plots below. Only fitted a small region near the
bifurcation (in accordance with Strogatz).

f-I-curve (inverse logarithmic fit near the homoclinic bifurcation; form
of the equation is taken from Izhikevich book, fig. 6.30 on p. 189):

[image: f-i-curve]
https://cloud.githubusercontent.com/assets/5103165/11911101/0c3a114c-a60b-11e5-88df-4daf86eaed9b.png

Amplitudes (square root fit near the supercritical Hopf):

[image: amplitudes]
https://cloud.githubusercontent.com/assets/5103165/11911103/10452a6a-a60b-11e5-9493-79d2083ac8ff.png

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#8 (comment)
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[jrieke]

par*: Great idea, will do that!
mean: It's pretty regular, but I am averaging about a few spikes anyway (disregarding the first and last few spikes of each current step). Will include a sentence saying that spiking is regular. Also want to polish the legend/label descriptions after I'm done with the important stuff.
inset: I had the same idea, will look into it after I've finished everything else.