PyCont: Convergence problem for a frequency response

[Anonymous]

Hi,

I'm trying to reproduce a frequency response plot for a duffing equation using Pycont - see here.

However my code fails to converge, when the response becomes partly unstable (when damping is below beta<0.10).

I hope someone can give me a hint of what I can do about this.

Thanks,
Henrik

My code is found below:

from PyDSTool import *
import matplotlib.pyplot as plt

# simulation parameters
maxNumPoints = 1e5
maxStepSize = 1e-2
stepSize    = 1e-3
minStepSize = 1e-6

# physical parameters
s = -1.0 # sigma = Omega-omega0 (detuning parameter)
o = 1.0  # omega0
g = 0.5  # gamma
q = 0.2  # q
b = 0.2  # beta

# Equilibrium curve
ustr = '-b*o*u+q/(2*o)*sin(v)' # amplitude
vstr = 's*u-3*g/(8*o)*u*u*u+q/(2*o)*cos(v)' # phase

DSargs = args(name='duffing')
DSargs.pdomain = {'s': [-1.0, 1.0]}  # domain boundaries
DSargs.pars = {'s': s, 'o': o, 'g': g, 'q': q, 'b': b}
DSargs.varspecs = {'u': ustr, 'v': vstr}
DSargs.ics = {'u': 0.01, 'v': 1.0}

testDS = Generator.Vode_ODEsystem(DSargs)

PyCont = ContClass(testDS)

PCargs = args(name='EQ1', type='EP-C')
PCargs.freepars = ['s']
PCargs.StepSize = stepSize
PCargs.MaxNumPoints = maxNumPoints
PCargs.MaxStepSize = maxStepSize
PCargs.MinStepSize = minStepSize
PCargs.LocBifPoints = ['LP', 'BP', 'B']
PCargs.StopAtPoints = ['B']
PCargs.verbosity = 2
PCargs.SaveEigen = True
PCargs.Corrector = 'Natural'
PyCont.newCurve(PCargs)

print 'Computing first equilibrium curve...'
start = clock()
PyCont['EQ1'].forward()
print 'done in %.3f seconds!' % (clock()-start)

# Plots
fig1 = plt.figure(num=1)
PyCont.display(('s', 'u'), stability=True, linewidth=0.5)
plt.grid(True)
plt.title('amplitude')
ymin, ymax = plt.ylim()
plt.ylim([-ymax, ymax])
fig1.show()

[Drew LaMar]

Hi, Henrik. The MoorePenrose corrector is much more stable. I changed the corrector as follows:

 PCargs.Corrector = 'MoorePenrose'

then modified beta to 0.05 to get the attached figure.

• Drew

[Anonymous]

Thanks a lot!

Can I find an overview of available correctors anywhere in the documentation?