def continue_equilibrium(init, params=None, **kwargs):
"""Continue equilibrium forwards and backwards in I from init point."""
kwargs.setdefault('PAR', add_default_params(params, exclude=['I']))
equilibrium = auto.run(init, c='equilibrium', **kwargs)
equilibrium += auto.run(init, c='equilibrium', DS='-', **kwargs)
equilibrium = auto.relabel(auto.merge(equilibrium)) # get single curve with unique labels
return equilibrium
def continue_bifurcation(init, continuation_param, continuation_param_uzstop=None, params=None, **kwargs):
"""Continue bifurcation point in init for changing continuation_param. """
kwargs.setdefault('PAR', add_default_params(params, exclude=['I', continuation_param]))
kwargs.setdefault('ICP', ['I', continuation_param, 'PERIOD'])
if continuation_param_uzstop is not None:
kwargs.setdefault('UZSTOP', {'I': [-20, 100], continuation_param: continuation_param_uzstop})
bifurcation_point = auto.run(init, c='2par', **kwargs)
bifurcation_point += auto.run(init, c='2par', DS='-', **kwargs)
bifurcation_point = auto.relabel(auto.merge(bifurcation_point))
return bifurcation_point
def twoDimension_Hopf(self, startState, continuationParams, stopDictList = [{'gL':10, 'Cm':50, 'I':400}, {'gL':0.1, 'Cm':10, 'I':0.1}]):
global relevantHopf
# locus continuation of the interesting points, requires then two parameters for continuation
self.bifpar['I'] = startState['I']
numberOfIterations = 20
numberOfPlots = 1
directionList = [1, -1]
r = [0 for item in directionList]
direction = 1
r[0] = auto.run(startState, e='nak', c='nak',
parnames= self.pnames, unames=self.unames,
ICP=continuationParams,
ISP=2,ILP=1, #SP=['LP','HB','BP'], # ISP: Bifurcation detection; 0=off, 1=BP(FP), 3=BP(PO,BVP), 2=all | ILP: Fold detection; 1=on, 0=off
ISW=2, # ISW: Branch switching; 1=normal, -1=switch branch (BP, HB, PD), 2=switch to two-parameter continuation (LP, BP, HB, TR), 3=switch to three-parameter continuation (BP)
ITNW=17, NWTN=13, NMX=numberOfIterations, NPR= 1,#int(numberOfIterations/numberOfPlots),PAR=self.bifpar,
DS=direction*1e-1, DSMAX=1e-1, #STOP=[''],#STOP=['HB1'],
UZSTOP= {}#stopDictList[i] # e.g. UZSTOP_criterium={'gNa':15, 'gK':1, 'gK':12, 'V3':-10, 'V3':30, 'V1':-10, 'V1':30}
)
ipdb.set_trace()
if True:
print "Limit direction in twoDimension_Hopf" # this can give trouble when running into the BT, then it does not stop
direction = -1
numberOfIterations =2000
numberOfPlots = 1
DSMAX = 1.5e-1 # adapt this, smaller to find GH, larger to prevent that the continuation gets into an infinite loop at the BT
#if self.get_parameter('gL')>=0.2: DSMAX = 5e-1 # adapt this, smaller to find GH, larger to prevent that the continuation gets into an infinite loop at the BT
r[1] = auto.run(startState, e='nak', c='nak',
parnames= self.pnames, unames=self.unames,
ICP=continuationParams,
ISP=2,ILP=1, #SP=['LP','HB','BP'], # ISP: Bifurcation detection; 0=off, 1=BP(FP), 3=BP(PO,BVP), 2=all | ILP: Fold detection; 1=on, 0=off
ISW=2, # ISW: Branch switching; 1=normal, -1=switch branch (BP, HB, PD), 2=switch to two-parameter continuation (LP, BP, HB, TR), 3=switch to three-parameter continuation (BP)
PAR=self.bifpar, ITNW=7, NWTN=3, NMX=numberOfIterations, NPR=int(numberOfIterations/numberOfPlots),
DS=direction*1e-1, DSMAX=DSMAX, #STOP=[''],#STOP=['HB1'],
UZSTOP= {}#stopDictList[i] # e.g. UZSTOP_criterium={'gNa':15, 'gK':1, 'gK':12, 'V3':-10, 'V3':30, 'V1':-10, 'V1':30}
#UZSTOP= {'Cm':0.08}continue_hopf
)
relevantHopf = r[1].getLabel(r[1].getLabels()[-1])[-1]
#relevantHopf = r1.getLabel('UZ')[0]
self.plottingBranches.append(auto.merge(r[0]+r[1]))
self.r_eval = r
else:
self.plottingBranches.append(r[0])
self.r_eval = [r[0]]
self.params = continuationParams
return self.plottingBranches[-1]
limit_branch_points = {
"dR": limit_branch_point("UZ5"),
"dH": limit_branch_point("UZ3"),
"dP": limit_branch_point("UZ8")
}
fold_points = {
"dR": fold_plot("UZ2"),
"dH": fold_plot("UZ4"),
"dP": fold_plot("UZ5")
}
execfile('dispersal_two_parameter_analyses.py')
dX_K_plot = auto.merge(dX_K_plot)
dX_dY_plot = auto.merge(dX_dY_plot)
start_point_analysis = auto.merge(start_point_analysis)
auto.rl(start_point_analysis)
#Plots to look at the raw bifurcation diagrams in python. Comment out these
#commands if you don't want plots. Not needed for making final diagrams
auto.plot(start_point_analysis,
stability=True,
use_labels=False,
bifurcation_x=['K'],
bifurcation_y=['MAX H_1'],
coloring_method="type",
use_symbols=False,
grid=False)
limit_branch_points = {"dR":limit_branch_point("UZ5"),
"dH":limit_branch_point("UZ3"),
"dP":limit_branch_point("UZ8")
}
fold_points = {"dR":fold_plot("UZ2"),
"dH":fold_plot("UZ4"),
"dP":fold_plot("UZ5")
}
execfile('dispersal_two_parameter_analyses.py')
dX_K_plot =auto.merge(dX_K_plot)
dX_dY_plot =auto.merge(dX_dY_plot)
start_point_analysis = auto.merge(start_point_analysis)
auto.rl(start_point_analysis)
#Plots to look at the raw bifurcation diagrams in python. Comment out these
#commands if you don't want plots. Not needed for making final diagrams
auto.plot(start_point_analysis,
stability=True,use_labels=False,
bifurcation_x= ['K'],bifurcation_y= ['MAX H_1'],
coloring_method = "type", use_symbols= False,
grid = False)
auto.plot(dispersal_fixed_points,
stability=True,use_labels=False,
bifurcation_x= ['dR'],bifurcation_y= ['H_1'],