def compute_limit_cycle(self):
PCargs = args()
PCargs.name = 'LC1'
PCargs.type = 'LC-C'
PCargs.MaxNumPoints = 2500 # // 10
PCargs.NumIntervals = 30
PCargs.NumCollocation = 6
PCargs.initpoint = 'EQ1:H1'
PCargs.SolutionMeasures = 'all'
PCargs.NumSPOut = 200
PCargs.FuncTol = 1e-4
PCargs.VarTol = 1e-4
PCargs.TestTol = 1e-3
PCargs.SaveEigen = True
self.pc.newCurve(PCargs)
print('Computing limit-cycle curve...')
start = perf_counter()
self.pc['LC1'].forward()
# PyCont['LC1'].backward()
print('done in %.3f seconds!' % (perf_counter() - start))
# Get the lower branch of the cycle.
self.pc['LC1'].display(('mu', 'R_min'), stability=True, figure=1)
self.pc['LC1'].display(('mu', 'R'), stability=True, figure=1)
self.pc['LC1'].display(stability=True, figure='new', axes=(1, 2, 1))
self.pc['LC1'].plot_cycles(coords=('R', 'r'),
linewidth=1,
axes=(1, 2, 2),
figure='fig2')
def _limit_cycle_curve(self, pars, index=-1):
(name, PyCont) = self.cont_classes[index]
# Limit cycle curve
PCargs = args(freepars=PyCont[name].freepars)
PCargs.name = 'LC1'
PCargs.type = 'LC-C'
PCargs.MaxNumPoints = 2500 # // 10
PCargs.NumIntervals = 20
PCargs.NumCollocation = 6
PCargs.initpoint = name + ':H1'
PCargs.SolutionMeasures = 'all'
PCargs.NumSPOut = 50
PCargs.FuncTol = 1e-10
PCargs.VarTol = 1e-10
PCargs.TestTol = 1e-8
PyCont.newCurve(PCargs)
print('Computing limit-cycle curve...')
start = perf_counter()
PyCont['LC1'].backward()
PyCont['LC1'].forward()
print('done in %.3f seconds!' % (perf_counter() - start))
PyCont['LC1'].display(pars, stability=True)
PyCont['LC1'].display((pars[0], pars[1] + '_min'), stability=True)
# TODO(matthew-c21): Keep track of associated figures.
PyCont['LC1'].display(stability=True, figure='new', axes=(1, 2, 1))
PyCont['LC1'].plot_cycles(coords=('R', 'r'),
linewidth=1,
axes=(1, 2, 2),
figure='fig2')
pass
def compute_HO(self, initpoint='', name='HO1', ax=None, p1='a1', p2='a2'):
PCargs = args()
PCargs.name = name
PCargs.type = 'H-C2'
PCargs.initpoint = initpoint
PCargs.freepars = [p1, p2]
PCargs.MaxNumPoints = 800
PCargs.MinStepSize = 1e-5
PCargs.MaxStepSize = 1e-2
PCargs.StepSize = 1e-3
PCargs.LocBifPoints = 'all'
PCargs.SaveEigen = True
self.pc.newCurve(PCargs)
print('Computing Hopf curve...')
start = perf_counter()
# PyCont[name].forward()
self.pc[name].backward()
print('done in %.3f seconds!' % (perf_counter() - start))
#PCargs.MaxNumPoints = 2000
# PyCont[name].forward()
self.pc[name].display([p1, p2], figure=3)
sol = self.pc[name].sol
a1 = sol.coordarray[sol.coordnames.index(p1)]
b1 = sol.coordarray[sol.coordnames.index(p2)]
if not ax:
fig, ax = plt.subplots(figsize=(4, 4))
fig.subplots_adjust(left=.2, bottom=0.17, right=0.98)
ax.plot(a1, b1, label=name)
return ax
def compute(self, pcargs, msg=None):
self.pc.newCurve(pcargs)
if msg is not None:
print(msg)
start = perf_counter()
self.pc[pcargs.name].forward()
print('Time elapsed: %.3f' % (perf_counter() - start))
else:
self.pc[pcargs.name].forward()
def display_cont_class(self, pars, index=-1):
(name, PyCont) = self.cont_classes[index]
# Go ahead and compute it upon registration
print('Computing curve...')
start = perf_counter()
PyCont[name].backward()
PyCont[name].forward()
print('done in %.3f seconds!' % (perf_counter() - start))
PyCont[name].display(pars, figure='new')
PyCont.plot.toggleAll('off', bytype='P')
if PyCont[name].getSpecialPoint('H1'):
self._limit_cycle_curve(pars, index)
#PCargs.StepSize = 3e-6
#PCargs.MaxStepSize = 3e-5
#PCargs.MinStepSize = 3e-7
PCargs.StepSize = 3e-4
PCargs.MaxStepSize = 3e-3
PCargs.MinStepSize = 3e-5
#PCargs.MaxNumPoints = 8000
PCargs.MaxNumPoints = 500
PCargs.LocBifPoints = 'all'
PCargs.verbosity = 2
#PCargs.StopAtPoints = ['H2']
#PCargs.StopAtPoints = ['H1']
PyCont.newCurve(PCargs)
print('Computing curve...')
start = perf_counter()
PyCont['EQ1'].forward()
# PyCont['EQ1'].backward()
print('done in %.3f seconds!' % (perf_counter()-start))
PyCont['EQ1'].display(('mu', 'R'), figure='new')
PyCont.plot.toggleAll('off', bytype='P')
if PyCont['EQ1'].getSpecialPoint('H1'):
if 0: # Limit cycle curve
PCargs.name = 'LC1'
PCargs.type = 'LC-C'
PCargs.MaxNumPoints = 2500 # // 10
PCargs.NumIntervals = 30
PCargs.NumCollocation = 6
PCargs.initpoint = 'EQ1:H1'