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issue with Lyapunov coefficients computations

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dupont
2013-05-28
2013-11-04
  • dupont
    dupont
    2013-05-28

    Hi,

    I am trying to move from Matcont to pydstool and I am not sure about the results from pydstool. I have been using the same equations and the pydstool seem to be missing some Generalized Hopf bifircation points. There should be two additional GH points at the x-axis values roughly -1 and 3 respectively. Has anyone gotten any similar issue?

    Thank you for your help.

    Here is my code

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    #! /opt/local/bin/python2.6
    # -*- coding: utf-8 -*-
    """
    Created on Wed May 22 15:03:55 2013
    """
    class bcolors:
        HEADER = '\033[95m'
        OKBLUE = '\033[94m'
        OKGREEN = '\033[92m'
        WARNING = '\033[93m'
        FAIL = '\033[91m'
        ENDC = '\033[0m'
        def disable(self):
            self.HEADER = ''
            self.OKBLUE = ''
            self.OKGREEN = ''
            self.WARNING = ''
            self.FAIL = ''
            self.ENDC = ''
            
    from PyDSTool import *
    from scipy.special import *
    import sys
    pars = {'Jee': 10.0,
            'Jei': -12.0,
            'Jie': 10.0,
            'Jii': -10.0,
            'tauE': 0.375,
            'tauI': 1.0,
            'Ii': 1.0,
            'Ee': 2.5,
            'alpha': 4.0}
    auxfndict = {'S': (['v'], '1.0/(1.0 + exp(-v))'), \
               'L': (['v'], 'log(1.0+exp(v))'), \
                 'Q': (['v'],'log(1.0+exp(v*10.0-.0))/10.20')   
                }
       
    icdict = {'E': 0.0,
              'I': 0.0}
    Estr = '(-E+S(Jee*E+Jei*I+Ee))/tauE'
    Istr = '(-I+S(Jie*E+Jii*I+Ii))/tauI'   
    ###############################################################################
    # parameter
    ###############################################################################
    DSargs = args(name='ISN97')
    DSargs.pars = pars
    DSargs.varspecs = {'E': Estr, 'I': Istr}
    DSargs.fnspecs = auxfndict
    DSargs.ics = icdict
    ###############################################################################
    # find IC
    ###############################################################################
    DSargs.tdomain = [0,200]
    DSargs.pdomain = {'Ii': [-4,7], 'Ee': [-2, 6]}
    DSargs.algparams = {'init_step' :0.01, 'strictopt':False}
    testDS = Generator.Vode_ODEsystem(DSargs)
    print 'Integrating...'
    start = clock()
    testtraj = testDS.compute('testDS')
    print '  ... finished in %.3f seconds.\n' % (clock()-start)
    if 1:
        plotData=testtraj.sample(dt=0.01)
        mline=plot(plotData['t'],plotData['E'])
        show()
    ###############################################################################
    # perform coninuation
    ###############################################################################
    # Set up continuation class
    PyCont = ContClass(testDS)
    PCargs = args(name='EQ1', type='EP-C')
    PCargs.freepars = ['Ii']
    PCargs.StepSize = 1e-4
    PCargs.MinStepSize = 1e-4
    PCargs.MaxNumPoints = 2000
    PCargs.MaxStepSize = 5e-2
    PCargs.LocBifPoints = 'all'
    PCargs.verbosity = 2
    PCargs.SaveEigen = True
    PCargs.pdomain = {'Ii': [-4,7], 'Ee': [-4, 6]}
    PyCont.newCurve(PCargs)
    print bcolors.WARNING + '--> Computing EQ1...'+ bcolors.ENDC 
    start = clock()
    PyCont['EQ1'].forward()
    PyCont['EQ1'].backward()
    print 'done in %.3f seconds!' % (clock()-start)
    if 1:
        PyCont.display(('Ee','I'),stability=True);
        show()
    #sys.exit()
    ###############################################################################
    # courbe des Hopfs
    ###############################################################################
    print '--> Hopf Curve ...'
    PCargs = args(name='HO1', type='H-C2')
    PCargs.initpoint = 'EQ1:H1'
    PCargs.freepars = ['Ee', 'Ii']
    PCargs.MaxNumPoints = 100
    PCargs.LocBifPoints = 'all'
    PCargs.verbosity = 2
    PyCont.newCurve(PCargs)
    print 'Computing Hopf curve...'
    start = clock()
    PyCont['HO1'].forward()
    print '----> backward'
    PyCont['HO1'].backward()
    print 'done in %.3f seconds!' % (clock()-start)
    PyCont['HO1'].display(('Ee','Ii'),stability=True);
    ###############################################################################
    # courbe des Hopfs
    ###############################################################################
    print '--> Hopf Curve #2 ...'
    PCargs = args(name='HO2', type='H-C2')
    PCargs.initpoint = 'EQ1:H2'
    PCargs.freepars = ['Ee', 'Ii']
    PCargs.MaxNumPoints = 200
    PCargs.LocBifPoints = 'all'
    PCargs.verbosity = 2
    PyCont.newCurve(PCargs)
    print 'Computing Hopf curve...'
    start = clock()
    PyCont['HO2'].forward()
    print '----> backward'
    PyCont['HO2'].backward()
    print 'done in %.3f seconds!' % (clock()-start)
    PyCont['HO2'].display(('Ee','Ii'),stability=True);
    PyCont['HO1'].display(('Ee','Ii'),stability=True);grid();axis([-2,6,-6,6])
    ###############################################################################
    # courbe des LP
    ###############################################################################
    print '--> LP Curve ...'
    PCargs = args(name='LP1', type='LP-C')
    PCargs.initpoint = 'HO1:BT1'
    PCargs.freepars = ['Ee', 'Ii']
    PCargs.MaxNumPoints = 100
    PCargs.LocBifPoints = 'all'
    PCargs.verbosity = 2
    PyCont.newCurve(PCargs)
    print 'Computing Hopf curve...'
    start = clock()
    PyCont['LP1'].forward()
    PyCont['LP1'].backward()
    print 'done in %.3f seconds!' % (clock()-start)
    PyCont['HO2'].display(('Ee','Ii'),stability=True);
    PyCont['HO1'].display(('Ee','Ii'),stability=True);
    PyCont['LP1'].display(('Ee','Ii'),stability=True);
    show()
    print '--> LP Curve ...'
    PCargs = args(name='LP2', type='LP-C')
    PCargs.initpoint = 'HO2:BT2'
    PCargs.freepars = ['Ee', 'Ii']
    PCargs.MaxNumPoints = 100
    PCargs.LocBifPoints = 'all'
    PCargs.verbosity = 2
    PyCont.newCurve(PCargs)
    print 'Computing Hopf curve...'
    start = clock()
    PyCont['LP1'].forward()
    PyCont['LP1'].backward()
    print 'done in %.3f seconds!' % (clock()-start)
    ###############################################################################
    # Display
    ###############################################################################
    PyCont['HO2'].display(('Ee','Ii'),stability=True);
    PyCont['HO1'].display(('Ee','Ii'),stability=True);
    PyCont['LP1'].display(('Ee','Ii'),stability=True);
    PyCont['LP2'].display(('Ee','Ii'),stability=True);
    show()