Bifurcation Diagram Using Aux Variables

[Danny Wood]

I'm trying to plot a bifurcation diagram for a single neuron recurrent neural network. At the moment, I'm plotting the diagram of b against x, but really want to plot b against y (a non-linear but monotonic transformation of x). When I try changing "PC.display(['b','x'], stability=True, figure=3) " to 'y' instead of 'x' I get a key error saying "Coordinate y is not defined". Is there an easy solution to this?

import PyDSTool as dst
import numpy as np
from matplotlib import pyplot as plt

DSargs = dst.args(name="Single Neuron Network")

DSargs.pars = {
    'b' : -1,
    'w1' : 5
    }
DSargs.fnspecs = {'sigm': (['t'], '1 / (1 + exp(-t))')}
DSargs.varspecs = {'x': '-x + w1 * sigm(x) + b', 'w': 'x-w', 'y': 'sigm(x)'}
DSargs.auxvars = ['y']
DSargs.ics = {'x': -10, 'w':0}

DSargs.tdomain = [-5,5]
ode = dst.Generator.Vode_ODEsystem(DSargs)
traj = ode.compute('polarization')
pts = traj.sample(dt=0.1)

plt.plot(pts['t'], pts['x'])
plt.xlabel('time')                              
plt.ylabel('voltage')                          
plt.ylim([0,15])                              
plt.title(ode.name)                          
plt.show()

ode.set(pars = {'b': -6} )  

PC = dst.ContClass(ode)            

PCargs = dst.args(name='EQ1', type='EP-C')    
PCargs.freepars     = ['b']                  
PCargs.MaxNumPoints = 250                   
PCargs.MaxStepSize  = 1e-1
PCargs.MinStepSize  = 1e-4
PCargs.StepSize     = 1e-3
PCargs.LocBifPoints = 'LP'                
PCargs.SaveEigen    = True                 

PC.newCurve(PCargs)
PC['EQ1'].forward()
PC.display(['b','x'], stability=True, figure=3)        

plt.show()

[Danny Wood]

The solution I have at the moment is to apply the sigmoid function to X[1,:] inside the continuation class (and apply it to the special points too). However, this is a pretty hacky solution, even after I clean it up a bit. Is there a way of doing this without having to change any PyDSTool files?

[Drew LaMar]

Hi, Danny. It's been awhile since I've taken a look at the code, but I'm pretty sure that auxvars are not updated during continuation, at least in a way that they are accessible. Your solution is in effect something similar to what I would do to add this functionality, i.e. evaluate auxvars during continuation and bifurcation point detection.

Drew

[Rob Clewley]

Maybe what's best here, given our lack of resources, is for Danny to submit a PR for his code (with enough documentation for us to follow it) and we can attempt to clean it up as best as we can and make use of it.

[Danny Wood]

Thanks both. I'll try to submit a PR in the next day or so.

[Florian Aspart]

Hi all,

I already had a problem with auxiliary variables 2 years ago.
https://sourceforge.net/p/pydstool/discussion/472291/thread/58f70ac0/

It is actually a little bit more complicated than computing the auxiliary
variables in the plot function only.
Indeed this would work for EP-C curves but not for Limit cycle curves. The
problem is that PyCont does not give back the whole limit cycle at each
points but only a some special points. The rest of the time only some
"statistics", e.g. min, max or average values of the limit cycle are
returned (cf the discussion 2 years ago).

Most importantly, the LP-C curve cannot be calculated if auxiliary
variables are used in the dynamical system. The #define line corresponding
to them are not added to the C source code for the Auto "integrator". I
fixed
https://github.com/F-A/pydstool/commit/3c34e2237e1f5a8f8743f67898849e582800a9b6
it 2 years ago and sent a PR to Drew, but I cannot find it in the current
version of the PyDSTool main repo.

Best,
Florian

2016-06-28 16:33 GMT+02:00 Danny Wood dwood04@users.sf.net:

Thanks both. I'll try to submit a PR in the next day or so.

Bifurcation Diagram Using Aux Variables
https://sourceforge.net/p/pydstool/discussion/472291/thread/cf2657ce/?limit=25#c421

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