def figure4b1_continuation():
"""Actual continuation analysis for 4B1. Contains commands to pyDSTool.
Performs some formatting and continuation.
Plotting commands are contained with continuation commands to keep pycont objects together
:return: None
"""
# Set parameters and convert to symbolic representation
parameters = default_parameters(i_app=0 * uA_PER_CM2)
striped_parameters = {k: strip_dimension(v) for k, v in parameters.items()}
v, h, i_app = symbols("v h i_app")
striped_parameters["i_app"] = i_app
dydt = ode_2d([v, h], 0, striped_parameters, exp=exp)
DSargs_1 = PyDSTool.args(name="bifn_1")
DSargs_1.pars = {"i_app": 0}
DSargs_1.varspecs = {
"v": PyDSTool.convertPowers(str(dydt[0])),
"h": PyDSTool.convertPowers(str(dydt[1])),
}
DSargs_1.ics = {"v": 0, "h": 0}
ode_1 = PyDSTool.Generator.Vode_ODEsystem(DSargs_1)
ode_1.set(pars={"i_app": 0})
ode_1.set(ics={"v": -49, "h": 0.4})
PyCont_1 = PyDSTool.ContClass(ode_1)
PCargs_1 = PyDSTool.args(name="EQ1_1", type="EP-C")
PCargs_1.freepars = ["i_app"]
PCargs_1.MaxNumPoints = 500
PCargs_1.MaxStepSize = 0.05
PCargs_1.MinStepSize = 1e-5
PCargs_1.StepSize = 1e-2
PCargs_1.LocBifPoints = "all"
PCargs_1.SaveEigen = True
PyCont_1.newCurve(PCargs_1)
PyCont_1["EQ1_1"].backward()
PyCont_1["EQ1_1"].forward()
PyCont_1["EQ1_1"].backward()
PyCont_1["EQ1_1"].display(["i_app", "v"], stability=True, figure=1)
PCargs_1.name = "LC1_1"
PCargs_1.type = "LC-C"
PCargs_1.initpoint = "EQ1_1:H1"
PCargs_1.freepars = ["i_app"]
PCargs_1.MaxNumPoints = 500
PCargs_1.MaxStepSize = 0.1
PCargs_1.LocBifPoints = "all"
PCargs_1.SaveEigen = True
PyCont_1.newCurve(PCargs_1)
PyCont_1["LC1_1"].backward()
PyCont_1["LC1_1"].display(("i_app", "v_min"), stability=True, figure=1)
PyCont_1["LC1_1"].display(("i_app", "v_max"), stability=True, figure=1)
PyCont_1.plot.toggleLabels(visible="off", bytype=["P", "RG", "LP"])
PyCont_1.plot.togglePoints(visible="off", bytype=["P", "RG", "LP"])
plt.gca().set_title("")
def get_pycont(param_dict):
DSargs = dst.args(name='Whi5_Sbf_module')
# parameters
DSargs.pars = {
"kasSW": 1.67,
"kdisSW": 1.67e-4,
"kPhWhi5": 1e-3,
"kDphWhi5": 5e-4,
"fac": 58,
"kdCln12": 0.0015,
"Sbft": 1.1,
"Whi50": 65,
"V": 20,
"Cln3": 1.0
}
DSargs.varspecs = {
'Cln12': 'kdCln12*fac*Sbf/Sbft - kdCln12*Cln12',
'Sbf':
'-kasSW*(Whi50/V+Sbf-Sbft-Whi5P)*Sbf + (kdisSW + kPhWhi5*(Cln12+Cln3))*(Sbft-Sbf)',
'Whi5P': '(kPhWhi5*(Cln12+Cln3))*(Whi50/V-Whi5P) - kDphWhi5*Whi5P',
}
set_params_from_dict(DSargs.pars, param_dict)
DSargs.ics = get_steady_states(param_dict)
ode = dst.Generator.Vode_ODEsystem(DSargs)
return dst.ContClass(ode)
def __figure4b1_continuation__():
parameters = default_parameters(i_app=0)
v, h, i_app = symbols('v h i_app')
parameters[0] = i_app
dydt = ode_2d([v, h], 0, parameters, exp=exp)
DSargs_1 = PyDSTool.args(name='bifn_1')
DSargs_1.pars = {'i_app': 0}
DSargs_1.varspecs = {
'v': PyDSTool.convertPowers(str(dydt[0])),
'h': PyDSTool.convertPowers(str(dydt[1]))
}
DSargs_1.ics = {'v': 0, 'h': 0}
ode_1 = PyDSTool.Generator.Vode_ODEsystem(DSargs_1)
ode_1.set(pars={'i_app': 0})
ode_1.set(ics={'v': -49, "h": 0.4})
PyCont_1 = PyDSTool.ContClass(ode_1)
PCargs_1 = PyDSTool.args(name='EQ1_1', type='EP-C')
PCargs_1.freepars = ['i_app']
PCargs_1.MaxNumPoints = 500
PCargs_1.MaxStepSize = 0.05
PCargs_1.MinStepSize = 1e-5
PCargs_1.StepSize = 1e-2
PCargs_1.LocBifPoints = 'all'
PCargs_1.SaveEigen = True
PyCont_1.newCurve(PCargs_1)
PyCont_1['EQ1_1'].backward()
PyCont_1['EQ1_1'].forward()
PyCont_1['EQ1_1'].backward()
PyCont_1['EQ1_1'].display(['i_app', 'v'], stability=True, figure=1)
PCargs_1.name = 'LC1_1'
PCargs_1.type = 'LC-C'
PCargs_1.initpoint = 'EQ1_1:H1'
PCargs_1.freepars = ['i_app']
PCargs_1.MaxNumPoints = 500
PCargs_1.MaxStepSize = 0.1
PCargs_1.LocBifPoints = 'all'
PCargs_1.SaveEigen = True
PyCont_1.newCurve(PCargs_1)
PyCont_1['LC1_1'].backward()
PyCont_1['LC1_1'].display(('i_app', 'v_min'), stability=True, figure=1)
PyCont_1['LC1_1'].display(('i_app', 'v_max'), stability=True, figure=1)
PyCont_1.plot.toggleLabels(visible='off', bytype=['P', 'RG'])
PyCont_1.plot.togglePoints(visible='off', bytype=['P', 'RG'])
plt.gca().set_title('')
def __figure4b2_continuation__():
parameters = default_parameters(i_app=-0.1)
v, h, h_s, i_app = symbols('v h h_s i_app')
parameters[0] = i_app
dydt = ode_3d([v, h, h_s], 0, parameters, exp=exp)
DSargs_2 = PyDSTool.args(name='bifn_2')
DSargs_2.pars = {'i_app': 0}
DSargs_2.varspecs = {
'v': PyDSTool.convertPowers(str(dydt[0])),
'h': PyDSTool.convertPowers(str(dydt[1])),
'h_s': PyDSTool.convertPowers(str(dydt[2]))
}
DSargs_2.ics = {'v': 0, 'h': 0, 'h_s': 0}
ode_2 = PyDSTool.Generator.Vode_ODEsystem(DSargs_2)
ode_2.set(pars={'i_app': -0.1})
ode_2.set(ics={'v': -67, "h": 0.77, "h_s": 1})
PyCont_2 = PyDSTool.ContClass(ode_2)
PCargs_2 = PyDSTool.args(name='EQ1_2', type='EP-C')
PCargs_2.freepars = ['i_app']
PCargs_2.MaxNumPoints = 300
PCargs_2.MaxStepSize = 0.1
PCargs_2.MinStepSize = 1e-5
PCargs_2.StepSize = 1e-2
PCargs_2.LocBifPoints = 'all'
PCargs_2.SaveEigen = True
PyCont_2.newCurve(PCargs_2)
PyCont_2['EQ1_2'].backward()
PyCont_2['EQ1_2'].display(['i_app', 'v'], stability=True, figure=1)
PCargs_2.name = 'LC1_2'
PCargs_2.type = 'LC-C'
PCargs_2.initpoint = 'EQ1_2:H2'
PCargs_2.freepars = ['i_app']
PCargs_2.MaxNumPoints = 400
PCargs_2.MaxStepSize = 0.1
PCargs_2.StepSize = 1e-2
PCargs_2.LocBifPoints = 'all'
PCargs_2.SaveEigen = True
PyCont_2.newCurve(PCargs_2)
PyCont_2['LC1_2'].forward()
PyCont_2['LC1_2'].display(('i_app', 'v_min'), stability=True, figure=1)
PyCont_2['LC1_2'].display(('i_app', 'v_max'), stability=True, figure=1)
PyCont_2.plot.toggleLabels(visible='off', bytype=['P', 'RG'])
PyCont_2.plot.togglePoints(visible='off', bytype=['P', 'RG'])
plt.gca().set_title('')
def __figure3c_continuation__():
parameters = default_parameters(i_app=0.16)
v, h, h_s = symbols('v h h_s')
dydt = hs_clamp([v, h, h_s], 0, parameters)
DSargs_3 = PyDSTool.args(name='bifn_3')
DSargs_3.pars = {'h_s': 0}
DSargs_3.varspecs = {
'v': PyDSTool.convertPowers(str(dydt[0])),
'h': PyDSTool.convertPowers(str(dydt[1]))
}
DSargs_3.ics = {'v': 0, 'h': 0}
ode_3 = PyDSTool.Generator.Vode_ODEsystem(DSargs_3)
ode_3.set(pars={'h_s': 0})
ode_3.set(ics={'v': -49, "h": 0.4})
PyCont_3 = PyDSTool.ContClass(ode_3)
PCargs_3 = PyDSTool.args(name='EQ1_3', type='EP-C')
PCargs_3.freepars = ['h_s']
PCargs_3.MaxNumPoints = 350
PCargs_3.MaxStepSize = 0.1
PCargs_3.MinStepSize = 1e-5
PCargs_3.StepSize = 1e-2
PCargs_3.LocBifPoints = 'all'
PCargs_3.SaveEigen = True
PyCont_3.newCurve(PCargs_3)
PyCont_3['EQ1_3'].backward()
PyCont_3['EQ1_3'].display(['h_s', 'v'], stability=True, figure=1)
PCargs_3.name = 'LC1_3'
PCargs_3.type = 'LC-C'
PCargs_3.initpoint = 'EQ1_3:H2'
PCargs_3.freepars = ['h_s']
PCargs_3.MaxNumPoints = 500
PCargs_3.MaxStepSize = 0.1
PCargs_3.LocBifPoints = 'all'
PCargs_3.SaveEigen = True
PyCont_3.newCurve(PCargs_3)
PyCont_3['LC1_3'].backward()
PyCont_3['LC1_3'].display(('h_s', 'v_min'), stability=True, figure=1)
PyCont_3['LC1_3'].display(('h_s', 'v_max'), stability=True, figure=1)
PyCont_3.plot.toggleLabels(visible='off', bytype=['P', 'RG'])
PyCont_3.plot.togglePoints(visible='off', bytype=['P', 'RG'])
plt.gca().set_title('')
print "\n"
print "STEADY-STATES (NUMERICAL)"
print ss
#---Bifurcation Diagram
DSargs.ics = {
'xC': ss[1][xC],
'xB': ss[1][xB],
'xT': ss[1][xT],
'xW': ss[1][xW]
}
ode = PyDSTool.Generator.Vode_ODEsystem(DSargs)
PyCont = PyDSTool.ContClass(ode)
bifPar = 'aT'
PCargs = PyDSTool.args(name='EQ1', type='EP-C')
PCargs.freepars = [bifPar]
PCargs.StepSize = 1e0
PCargs.MaxNumPoints = 200
PCargs.MaxStepSize = 1e0
PCargs.LocBifPoints = 'all'
PCargs.SaveEigen = True
print("Calculating EQ1 curve ...")
PyCont.newCurve(PCargs)
PyCont['EQ1'].forward()
PyCont['EQ1'].backward()
import PyDSTool
#from numpy import (sin, cos, pi)
#from PyDSTool.Toolbox import phaseplane as pp
#import numpy as np
import matplotlib.pyplot as plt
from rhc_cont import Ode
import pickle
from bmk import Bmk
#from ode import Ode
from rhc_cont import RhcCont
bmk = Bmk({'ox': 0, 'oy': 0})
ode = bmk.get_ode()
#Setting Continuation class
PC = PyDSTool.ContClass(ode)
##########################################################
#
#
#
##########################################################
def inner_outer_init(PC):
print("Initialising boundary")
PCargs = PyDSTool.args(name='EQ1', type='EP-C')
PCargs.freepars = ['ox']
PCargs.MaxNumPoints = 200
PCargs.MaxStepSize = 0.001
PCargs.LocBifPoints = 'LP'
for i, v0 in enumerate(np.linspace(-80, 80, 20)):
ode.set(ics={'v': v0}) # Initial condition
# Trajectories are called pol0, pol1, ...
# sample them on the fly to create Pointset tmp
tmp = ode.compute('pol%3i' % i).sample()
plt.plot(tmp['t'], tmp['v'])
plt.xlabel('time')
plt.ylabel('voltage')
plt.title(ode.name + ' multi ICs')
# Prepare the system to start close to a steady state
ode.set(pars={'i': -220}) # Lower bound of the control parameter 'i'
ode.set(ics={'v':
-170}) # Close to one of the steady states present for i=-220
PC = dst.ContClass(ode) # Set up continuation class
PCargs = dst.args(
name='EQ1', type='EP-C'
) # 'EP-C' stands for Equilibrium Point Curve. The branch will be labeled 'EQ1'.
PCargs.freepars = [
'i'
] # control parameter(s) (it should be among those specified in DSargs.pars)
PCargs.MaxNumPoints = 450 # The following 3 parameters are set after trial-and-error
PCargs.MaxStepSize = 2
PCargs.MinStepSize = 1e-5
PCargs.StepSize = 2e-2
PCargs.LocBifPoints = 'LP' # detect limit points / saddle-node bifurcations
PCargs.SaveEigen = True # to tell unstable from stable branches
PC.newCurve(PCargs)
def SPoCK_bifurcation(alt_ics_dict):
pardict, fndict, vardict, icsdict = init_SPoCK()
DSargs = dst.args()
DSargs.pars = pardict
DSargs.varspecs = vardict
DSargs.fnspecs = fndict
DSargs.ics = alt_ics_dict
DSargs.name = 'SPoCK'
DSargs.tdata = [0, 10000]
DSargs.xdomain = {
'X': [0, 10**9],
'Y': [0, 10**9],
'A': [0, 10**9],
'B': [0, 10**9],
}
spock_ode = dst.Vode_ODEsystem(DSargs)
#spock_ode.set(pars = {'w': 1} ) # Lower bound of the control parameter 'i'
#traj = spock_ode.compute('test_trj') # integrate ODE
# setup continuation class
PC = dst.ContClass(spock_ode)
PCargs = dst.args(name='EQ1', type='EP-C')
PCargs.freepars = ['A_c']
PCargs.StepSize = 10
PCargs.MaxNumPoints = 10000
PCargs.MaxStepSize = 20
PCargs.MinStepSize = 10
PCargs.MaxTestIters = 10000
PCargs.LocBifPoints = 'all'
PCargs.SaveEigen = True
PCargs.verbosity = 2
PC.newCurve(PCargs)
PC['EQ1'].backward()
print(PC['EQ1'].info())
PCargs = dst.args(name='EQ2', type='EP-C')
PCargs.initpoint = 'EQ1:H1'
PCargs.freepars = ['A_c']
PCargs.StopAtPoints = ['BP']
PCargs.MaxNumPoints = 10
PCargs.MaxStepSize = 20
PCargs.MinStepSize = 10
PCargs.StepSize = 10
PCargs.LocBifPoints = 'all'
PCargs.SaveEigen = True
PC.newCurve(PCargs)
PC['EQ2'].forward()
plot_out_path = "/Users/behzakarkaria/Documents/UCL/Barnes Lab/PhD Project/research_code/SPoCK_model/parameter_csv/fixedpoint_plots/"
with PdfPages(plot_out_path + "bifurcation_Ac_X" + ".pdf") as pdf:
fig1 = plt.figure(1)
ax = fig1.add_subplot(figsize=(18, 12.5))
#ax.set_xlim(10**0, 10**9)
#ax.set_ylim(10**0, 10**9)
#ax.set_xscale('symlog', basex=10)
#ax.set_yscale('symlog', basey=10)
PC.display(('A_c', 'X'), stability=True)
pdf.savefig(fig1)
with PdfPages(plot_out_path + "bifurcation_Ac_Y" + ".pdf") as pdf:
fig2 = plt.figure(2)
fig2.add_subplot(figsize=(18, 12.5))
ax2 = plt.gca()
#ax2.set_xlim(0, 10**9)
#ax2.set_ylim(0, 10**9)
#ax2.set_xscale('symlog', basex=10)
#ax2.set_yscale('symlog', basey=10)
PC.display(('A_c', 'X'), stability=True, figure=fig2)
pdf.savefig(ax2.get_figure())
plt.xlabel('time') # Axes labels
plt.ylabel('x')
plt.show()
plt.plot(pts['x'], pts['y'])
plt.xlabel('x') # Axes labels
plt.ylabel('y')
plt.show()
# plot vector field, using a scale exponent to ensure arrows are well spaced
# and sized
pp.plot_PP_vf(ode, 'x', 'y', scale_exp=-1, N=50)
plt.show()
PyCont = dst.ContClass(ode)
PCargs = dst.args(name='EQ1', type='EP-C')
PCargs.freepars = ['mu']
PCargs.StepSize = 0.1
PCargs.MaxNumPoints = 50
PCargs.MaxStepSize = 2
PCargs.MinStepSize = 1e-5
PCargs.LocBifPoints = ['all']
PCargs.verbosity = 2
PCargs.SaveEigen = True
#PCargs.StopAtPoints = 'B'
PyCont.newCurve(PCargs)
print('Computing curve...')
start = dst.clock()
def figure3c_continuation():
"""Continuation analysis for 3C. Contains commands to pyDSTool.
Performs some formatting and continuation
Plotting commands are contained with continuation commands to keep pycont objects together
:return: None
"""
# Set parameters and convert to symbolic representation
parameters = default_parameters(i_app=0.16 * uA_PER_CM2)
striped_parameters = {k: strip_dimension(v) for k, v in parameters.items()}
v, h, h_s = symbols("v h h_s")
dydt = hs_clamp(
[v, h, h_s], 0, striped_parameters
) # returns a symbolic expression since variables are symbolic
DSargs_3 = PyDSTool.args(name="bifn_3")
DSargs_3.pars = {"h_s": 0}
DSargs_3.varspecs = {
"v": PyDSTool.convertPowers(str(dydt[0])),
"h": PyDSTool.convertPowers(str(dydt[1])),
} # convert **2 to ^2
DSargs_3.ics = {"v": 0, "h": 0}
ode_3 = PyDSTool.Generator.Vode_ODEsystem(DSargs_3)
ode_3.set(pars={"h_s": 0})
ode_3.set(ics={"v": -49, "h": 0.4})
PyCont_3 = PyDSTool.ContClass(ode_3)
PCargs_3 = PyDSTool.args(name="EQ1_3", type="EP-C")
PCargs_3.freepars = ["h_s"]
PCargs_3.MaxNumPoints = 350
PCargs_3.MaxStepSize = 0.1
PCargs_3.MinStepSize = 1e-5
PCargs_3.StepSize = 1e-2
PCargs_3.LocBifPoints = "all"
PCargs_3.SaveEigen = True
PyCont_3.newCurve(PCargs_3)
PyCont_3["EQ1_3"].backward()
PyCont_3["EQ1_3"].display(["h_s", "v"], stability=True, figure=1)
PCargs_3.name = "LC1_3"
PCargs_3.type = "LC-C"
PCargs_3.initpoint = "EQ1_3:H2"
PCargs_3.freepars = ["h_s"]
PCargs_3.MaxNumPoints = 500
PCargs_3.MaxStepSize = 0.1
PCargs_3.LocBifPoints = "all"
PCargs_3.SaveEigen = True
PyCont_3.newCurve(PCargs_3)
PyCont_3["LC1_3"].backward()
PyCont_3["LC1_3"].display(("h_s", "v_min"), stability=True, figure=1)
PyCont_3["LC1_3"].display(("h_s", "v_max"), stability=True, figure=1)
PyCont_3.plot.toggleLabels(
visible="off", bytype=["P", "RG", "LPC"]
) # remove unused labels
PyCont_3.plot.togglePoints(
visible="off", bytype=["P", "RG", "LPC"]
) # remove unused points
# hopefully remove rightmost hopf point - this may not always be H1?
PyCont_3.plot.toggleLabels(visible="off", byname="H1")
plt.gca().set_title("")
# # sample them on the fly to create Pointset tmp
# trajIC = DS.compute('trajIC%i' %i).sample() # or specify dt option to sample to sub-sample
# pl.plot(trajIC['t'], trajIC['N'])
# pl.xlabel('time')
# pl.ylabel('N')
# pl.title(DS.name + ' multi ICs')
# pl.show()
#Analise de bifurcacao
#DS.set(pars = {'b': 0} ) # Lower bound of the control parameter
DS.set(ics={
'N': pointSet['N'][-1],
'P': pointSet['P'][-1]
}) # Close to one of the steady states -- pointSet['N'][-1] foi definido acima
PC = dst.ContClass(DS) # Set up continuation class
PCargs = dst.args(
) # 'EP-C' stands for Equilibrium Point Curve. The branch will be labeled 'EQ1'.
PCargs.name = 'EQ1'
PCargs.type = 'EP-C'
PCargs.freepars = [
'c'
] # control parameter(s) (it should be among those specified in DSargs.pars)
PCargs.MaxNumPoints = 100 # The following 3 parameters are set after trial-and-error
PCargs.MaxStepSize = 1
PCargs.MinStepSize = 1E-5
PCargs.StepSize = 2E-2
PCargs.LocBifPoints = 'all' # detect limit points / saddle-node bifurcations
PCargs.verbosity = 2
PCargs.SaveEigen = True # to tell unstable from stable branches
def compute_period(vkd=0.28, vk=1.0):
"""
Compute period of oscillations as a function of yrel for given value of O_K
Return dictionary: {'yrel': ndarray, 'T': ndarray}
"""
# First check / Default set
po_data = svu.loaddata('../data/fit_po.pkl')[0]
lr_data = svu.loaddata('../data/fit_lra.pkl')[0]
chi_data = svu.loaddata('../data/chi_fit_0_bee.pkl')[0]
# yrel = 1.45
# yrel = 1.4715 # vk=0.5
# yrel = 1.448 # vk=0.2
# yrel = 2.0
yrel = 1.3
c0 = 5.0
rc = 0.8 * lr_data[0]
ver = lr_data[1]
vbeta = 1.0
vdelta = chi_data[1]
v3k = 1.4 * chi_data[2]
r5p = chi_data[3]
# DAG metabolism parameters
OmegaKD = 0.33
vd = 0.45
OmegaD = 0.26
pars = gchidp_pars(d1=po_data[0],
d2=po_data[1],
d3=po_data[0],
d5=po_data[2],
a2=po_data[3],
c1=0.5,
rl=0.01,
KER=0.1,
rc=rc,
ver=ver,
Kkc=0.5,
Kkd=0.1,
Kdd=0.1,
c0=c0,
yrel=yrel,
vbeta=vbeta,
vdelta=vdelta,
v3k=v3k,
r5p=r5p,
vkd=vkd,
vk=vk,
OmegaKD=OmegaKD,
vd=vd,
OmegaD=OmegaD)
# Generate ODE system
DSargs = gchidp_model(pars)
DSargs.tdomain = [0, 20] # set the range of integration
ode = dst.Generator.Vode_ODEsystem(
DSargs) # an instance of the 'Generator' class
traj = ode.compute('steady') # Integrate ODE
sol = traj.sample() # Retrieve solution
# Intermediate plotting
# plt.plot(sol['t'],sol['gammaa'],'k-')
# plt.plot(sol['t'],sol['ca'],'k-')
# plt.plot(sol['t'],sol['dag'],'r-')
# plt.plot(sol['t'],sol['pkc'],'b-')
# Prepare the system to start close to a steady state
p0 = traj(DSargs.tdomain[1])
ode.set(pars={'yrel': yrel}) # Lower bound of the control parameter 'i'
ode.set(ics=p0) # Start from steady-state
# Generate PyCont object
PC = dst.ContClass(ode) # Set up continuation class
# EP-C
PCargs = dst.args(
name='EQ1', type='EP-C', force=True
) # 'EP-C' stands for Equilibrium Point Curve. The branch will be labeled 'EQ1'.
PCargs.freepars = [
'yrel'
] # control parameter(s) (it should be among those specified in DSargs.pars)
PCargs.MaxNumPoints = 300 # The following 3 parameters are set after trial-and-error
PCargs.MaxStepSize = 0.01
PCargs.MinStepSize = 1e-4
PCargs.StepSize = 1e-3
PCargs.VarTol = 1e-5
PCargs.FuncTol = 1e-5
PCargs.TestTol = 1e-5
PCargs.LocBifPoints = 'all' # detect limit points / saddle-node bifurcations
PCargs.SaveEigen = True # to tell unstable from stable branches
PC.newCurve(PCargs)
# Compute equilibria
print "Computing EQ-C"
PC['EQ1'].forward()
# PC['EQ1'].backward()
print "done!"
svu.savedata([PC], 'tmp_cont.pkl')
PC = svu.loaddata('tmp_cont.pkl')[0]
# LC-C
PCargs = dst.args(name='LC1', type='LC-C', force=True)
PCargs.initpoint = 'EQ1:H1'
PCargs.freepars = ['yrel']
PCargs.MaxNumPoints = 200
PCargs.MaxStepSize = 0.05
PCargs.MinStepSize = 0.01
PCargs.StepSize = 1e-3
# PCargs.VarTol = 1e-6
# PCargs.FuncTol = 1e-4
# PCargs.TestTol = 1e-5
PCargs.LocBifPoints = 'all'
#PCargs.NumSPOut = 50;
#PCargs.SolutionMeasures = ['max','min']
PCargs.SolutionMeasures = 'all'
PCargs.SaveEigen = True
PC.newCurve(PCargs)
# Compute Orbits
print "Computing LC-C"
PC['LC1'].forward()
# PC['LC1'].backward()
print "done!"
# Retrieve solution
T = PC['LC1'].sol['_T']
yrel = PC['LC1'].sol['yrel']
# Retrieve stabled and unstable branches
idx = np.asarray([
PC['LC1'].sol.labels['LC'][i]['stab']
for i in PC['LC1'].sol.labels['LC']
], 'S')
plt.plot(yrel[idx == 'S'], T[idx == 'S'], 'ko')
plt.show()
return {'yrel': yrel[idx == 'S'], 'T': T[idx == 'S']}
traj = net.compute('test')
pts = traj.sample()
display(pts)
plt.show()
origin = pt.Point({"x1": 0, "x2": 0, "x3": 0, "x4": 0})
fp = ptppfixedpoint_nD(net, origin)
print(fp.evals)
print(fp.stability)
## Continuation to explore stability
PC = pt.ContClass(net)
PCargs = args()
PCargs.name = "EQ1"
PCargs.type = "EP-C"
PCargs.freepars = ["g"]
PCargs.StepSize = 1e-3
PCargs.MaxNumPoints = 100
PCargs.MaxStepSize = 1e-1
PCargs.LocBifPoints = "all"
PCargs.verbosity = 1
PCargs.SaveEigen = True
PCargs.Corrector = "Natural"
PC.newCurve(PCargs)
PC["EQ1"].forward()