def main(argv):
a = -1.0
b = 1.0
c = 2.0
x0 = -0.7
y0 = 1.0
t0 = 0.0
tf = 15.0
dt = 1e-5
xBounds = [-10, 10]
yBounds = [-10, 10]
resultsFilename = "results/integrationA%fB%fC%fX0%fY0%f.npz" % (a, b, c,
x0, y0)
def deriv(t, z):
x = z[0]
y = z[1]
f = lambda x, y: a + x**2 - y
g = lambda x, y: b * x - c * y
xDot = f(x=x, y=y)
yDot = g(x=x, y=y)
return (np.array([xDot, yDot]))
integrator = ode(deriv).set_integrator('vode')
z0 = np.array([x0, y0])
integrator.set_initial_value(z0, t0)
zs = [z0]
times = [t0]
step = 0
t = t0
z = z0
successfulIntegration = True
while successfulIntegration and t<tf and \
xBounds[0]<=z[0] and z[0]<=xBounds[1] and\
yBounds[0]<=z[1] and z[1]<=yBounds[1]:
step = step + 1
if step % 10000 == 0:
print('Processing time %.05f out of %.02f (%.02f, %.02f)' %
(t, tf, z[0], z[1]))
sys.stdout.flush()
integrator.integrate(t + dt)
t = integrator.t
z = integrator.y
times.append(t)
zs.append(z.tolist())
timesArray = np.array(times)
zsArray = buildMatrixFromArraysList(arraysList=zs)
np.savez(resultsFilename, times=timesArray, zs=zsArray)
def main(argv):
if len(argv) != 5:
print("Usage %s <I> <label> <v0> <n0>" % argv[0])
return
i0 = float(argv[1])
label = argv[2]
v0 = float(argv[3])
n0 = float(argv[4])
t0 = 0.0
t1 = 5.0
tf = 40.0
dt = 1e-5
resultsFilename = 'results/integrationINapIKFig4-37%s.npz' % label
iPulseStrength = 0.0
iPulseWidth = 1 * dt
def i(t):
if t1 - iPulseWidth / 2 < t and t <= t1 + iPulseWidth / 2:
return (i0 + iPulseStrength)
return (i0)
iNapIKModel = INapIKModel.getLowThresholdInstance(i=i)
integrator = ode(iNapIKModel.deriv).set_integrator('vode')
y0 = [v0, n0]
integrator.set_initial_value(y0, t0)
ys = [y0]
times = [t0]
step = 0
t = t0
y = y0
successfulIntegration = True
while successfulIntegration and t < tf:
step = step + 1
if step % 10000 == 0:
print('Processing time %.05f out of %.02f (%.02f, %.02f)' %
(t, tf, y[0], y[1]))
sys.stdout.flush()
integrator.integrate(t + dt)
t = integrator.t
y = integrator.y
times.append(t)
ys.append(y.tolist())
timesArray = np.array(times)
ysArray = buildMatrixFromArraysList(arraysList=ys)
np.savez(resultsFilename, times=timesArray, ys=ysArray)
def main(argv):
v0 = -73.00
n0 = 0.0
t0 = 0.0
tf = 100.0
current0 = 40.0
currentf = 400.0
dt = 1e-3
resultsFilename = 'results/integrationINapIKFig4-37Ramp.npz'
iSlope = 360.0 / 100.0
def i(t, iSlope=iSlope):
return (current0 + iSlope * t)
iNapIKModel = INapIKModel.getLowThresholdInstance(i=i)
# integrator = ode(iNapIKModel.deriv).set_integrator('vode', max_step=dt)
integrator = ode(iNapIKModel.deriv).set_integrator('vode')
y0 = [v0, n0]
integrator.set_initial_value(y0, t0)
ys = [y0]
times = [t0]
currents = [i(t0)]
step = 0
t = t0
y = y0
successfulIntegration = True
while successfulIntegration and t < tf:
step = step + 1
if step % 10000 == 0:
print('Processing time %.05f out of %.02f (%.02f, %.02f)' %
(t, tf, y[0], y[1]))
sys.stdout.flush()
integrator.integrate(t + dt)
t = integrator.t
y = integrator.y
times.append(t)
ys.append(y.tolist())
currents.append(i(t))
timesArray = np.array(times)
ysArray = buildMatrixFromArraysList(arraysList=ys)
currentsArray = np.array(currents)
np.savez(resultsFilename,
times=timesArray,
ys=ysArray,
currents=currentsArray)
def main(argv):
a = 7.0 / 8.0
b = 2.0
c = 1.0
x0 = 0.6
y0 = 1.2
t0 = 0.0
tf = 15.0
dt = 1e-5
resultsFilenamePattern = "results/integrationA%fB%fC%fX0%fY0%f.npz"%\
(a, b, c, x0, y0)
def deriv(self, t, y):
x = y[0]
y = y[1]
f = lambda x, y: a + x**2 - y
g = lambda x, y: b * x - c * y
xDot = f(x=x, y=y)
yDot = f(x=x, y=y)
return (np.array([xDot, yDot]))
integrator = ode(deriv).set_integrator('vode')
y0 = np.array([x0, y0])
integrator.set_initial_value(y0, t0)
ys = [y0]
times = [t0]
step = 0
t = t0
y = y0
successfulIntegration = True
while successfulIntegration and t < tf:
step = step + 1
if step % 10000 == 0:
print('Processing time %.05f out of %.02f (%.02f, %.02f)' %
(t, tf, y[0], y[1]))
sys.stdout.flush()
integrator.integrate(t + dt)
t = integrator.t
y = integrator.y
times.append(t)
ys.append(y.tolist())
timesArray = np.array(times)
ysArray = buildMatrixFromArraysList(arraysList=ys)
np.savez(resultsFilename, times=timesArray, ys=ysArray)
def main(argv):
i0 = 10.0
v0 = -60.00
n0 = 0.0008
t0 = 0.0
tf = 140.0
dt = 1e-4
current0 = 0.0
timeWinToSearchForUnstableFocus = (10, 80)
iSlope = 30.0 / 100.0
def i(t, iSlope=iSlope):
return (current0 + iSlope * t)
iNapIKModel = INapIKModel.getLowThresholdInstance(i=i)
integrator = ode(iNapIKModel.deriv).set_integrator('vode', max_step=dt)
y0 = [v0, n0]
integrator.set_initial_value(y0, t0)
ys = [y0]
times = [t0]
stabilityType, eigenValues, jacobian = \
iNapIKModel.checkStability(v0=v0, n0=n0)
stabilityTypes = [stabilityType]
eigenValuesList = [eigenValues.tolist()]
jacobiansList = [jacobian.flatten().tolist()]
step = 0
t = t0
y = y0
successfulIntegration = True
while successfulIntegration and t < tf:
step = step + 1
if step % 10 == 0:
print('Processing time %.05f out of %.02f (i=%.02f)' %
(t, tf, i(t=t)))
sys.stdout.flush()
integrator.integrate(t + dt)
t = integrator.t
y = integrator.y
times.append(t)
ys.append(y.tolist())
v = y[0]
n = y[1]
stabilityType, eigenValues, jacobian = \
iNapIKModel.checkStability(v0=v, n0=n)
stabilityTypes.append(stabilityType)
eigenValuesList.append(eigenValues.tolist())
jacobiansList.append(jacobian.flatten().tolist())
timesArray = np.array(times)
ysArray = buildMatrixFromArraysList(arraysList=ys)
eigenValuesArray = buildMatrixFromArraysList(arraysList=eigenValuesList)
stabilityTypesArray = np.array(stabilityTypes)
unstableFocusIndices = np.where(
stabilityTypesArray == iNapIKModel.UNSTABLE_FOCUS)[0]
timeWinIndices = np.where(
np.logical_and(timeWinToSearchForUnstableFocus[0] <= timesArray,
timesArray <= timeWinToSearchForUnstableFocus[1]))[0]
validUnstableFocusIndices = np.intersect1d(ar1=unstableFocusIndices,
ar2=timeWinIndices)
bifurcationIndex = validUnstableFocusIndices[0]
iAtBifurcation = i(t=timesArray[bifurcationIndex])
jacobianAtBifurcation = np.reshape(a=jacobiansList[bifurcationIndex],
newshape=(2, 2))
print("Input current at bifurcation: %.08f" % iAtBifurcation)
print("V at bifurcation: %.08f" % (ysArray[0, bifurcationIndex]))
print("n at bifurcation: %.08f" % ysArray[1, bifurcationIndex])
print("Jacobian at bifurcation: [[%.08f,%.08f],[%.08f,%.08f]]" %
(jacobianAtBifurcation[0, 0], jacobianAtBifurcation[0, 1],
jacobianAtBifurcation[1, 0], jacobianAtBifurcation[1, 1]))
print("Eigenvalues at bifurcation: %.08f+j%.08f, %.08f+j%.08f" %
(eigenValuesArray[0, bifurcationIndex].real,
eigenValuesArray[0, bifurcationIndex].imag,
eigenValuesArray[1, bifurcationIndex].real,
eigenValuesArray[1, bifurcationIndex].imag))
plt.plot(i(timesArray), eigenValuesArray[0, :].real)
plt.xlabel("Input Current")
plt.ylabel("Real Part of Eigenvalues")
plt.axhline(y=0, color="grey")
plt.axvline(x=iAtBifurcation, color="grey")
plt.show()
pdb.set_trace()
