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## issue with Lyapunov coefficients computations

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dupont
2013-05-28
2013-11-04

• 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?

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167``` ```#! /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() ```