def kuramotos(): for i in range(n): yield ω + c/(n-1)*sum( sin(y(j,t-τ[i,j])-y(i)) for j in range(n) if A[j,i] )
def __init__(self, tau=17., n=10., beta=0.2, gamma=0.1, initial_condition=None, burn_in=500):
self.vectorizable = True
# Set system of equations
f = [- gamma * y(0) + beta * y(0, t-tau) / (1.0 + y(0, t-tau) ** n)]
self.dde = jitcdde(f)
# Set initial condition
if initial_condition is None:
y_initial = 0.5
dy = lambda y: -gamma * y + beta * y / (1.0 + y ** n)
dy_initial = dy(y_initial)
self.dde.add_past_point(0.0, np.array([y_initial]), np.array([dy_initial]))
self.dde.add_past_point(tau, np.array([1.0]), np.array([0.0]))
else:
for condition in initial_condition:
time, value, derivative = condition
self.dde.add_past_point(time, np.array([value]), np.array([derivative]))
# Prepare DDE
self.dde.generate_lambdas()
self.dde.set_integration_parameters()
# Run burn_in
self.burn_in = burn_in
self.dde.integrate_blindly(self.burn_in)
import unittest
import numpy as np
from scipy.stats import sem
from jitcdde import t, y, jitcdde_lyap
if platform.system() == "Windows":
compile_args = None
else:
from jitcxde_common import DEFAULT_COMPILE_ARGS
compile_args = DEFAULT_COMPILE_ARGS+["-g","-UNDEBUG"]
omega = np.array([0.88167179, 0.87768425])
delay = 4.5
f = [
omega[0] * (-y(1) - y(2)),
omega[0] * (y(0) + 0.165 * y(1)),
omega[0] * (0.2 + y(2) * (y(0) - 10.0)),
omega[1] * (-y(4) - y(5)) + 0.25 * (y(0,t-delay) - y(3)),
omega[1] * (y(3) + 0.165 * y(4)),
omega[1] * (0.2 + y(5) * (y(3) - 10.0))
]
test_parameters = {
"rtol": 1e-7,
"atol": 1e-7,
"pws_rtol": 1e-3,
"pws_atol": 1e-3,
"first_step": 30,
"max_step": 100,
"min_step": 1e-30,
:linenos: Note that `integrate` does not only return local Lyapunov exponents but also the length of the time interval to which they apply (which differs from the time spanned by the `integrate` command and may even be zero). This length should be used to weigh the local Lyapunov exponents for statistical processing, like in line 31. """ if __name__ == "__main__": from jitcdde import jitcdde_lyap, y, t import numpy from scipy.stats import sem τ = 15 n = 10 β = 0.25 γ = 0.1 f = [ β * y(0,t-τ) / (1 + y(0,t-τ)**n) - γ*y(0) ] n_lyap = 4 DDE = jitcdde_lyap(f, n_lyap=n_lyap) DDE.constant_past([1.0]) DDE.step_on_discontinuities(max_step=1.0) data = [] lyaps = [] weights = [] for time in numpy.arange(DDE.t, DDE.t+10000, 10): state, lyap, weight = DDE.integrate(time) data.append(state) lyaps.append(lyap) weights.append(weight)
#!/usr/bin/python3
# -*- coding: utf-8 -*-
from jitcdde import jitcdde, y, t
import numpy
f = [ -y(0,t-2-y(0)**2) + 5 ]
DDE = jitcdde(f,max_delay=1e10)
eps = 0.1
DDE.add_past_point(-2.0 , [ 4.5], [0.0])
DDE.add_past_point(-1.0-eps, [ 4.5], [0.0])
DDE.add_past_point(-1.0+eps, [-0.5], [0.0])
DDE.add_past_point( 0.0 , [-0.5], [0.0])
DDE.integrate_blindly(0.01)
data = []
for time in numpy.arange(0,2.0,0.001)+DDE.t:
data.append([time, DDE.integrate(time)])
numpy.savetxt("timeseries.dat", data)
compile_args = None
else:
from jitcxde_common import DEFAULT_COMPILE_ARGS
compile_args = DEFAULT_COMPILE_ARGS+["-g","-UNDEBUG"]
a = -0.025794
b = 0.01
c = 0.02
τ = 1.0
k = Symbol("k")
scenarios = [
{
"f":
[
y(0)*(a-y(0))*(y(0)-1.0) - y(3) + k*(y(1)-y(0)),
y(1)*(a-y(1))*(y(1)-1.0) - y(4) + k*(y(2)-y(1)),
y(2)*(a-y(2))*(y(2)-1.0) - y(5) + k*(y(0)-y(2)),
b*y(0) - c*y(3,t-τ),
b*y(1) - c*y(4,t-τ),
b*y(2) - c*y(5,t-τ),
],
"vectors":
[
( [1.,1.,1.,0.,0.,0.], [0.,0.,0.,0.,0.,0.] ) ,
( [0.,0.,0.,0.,0.,0.], [1.,1.,1.,0.,0.,0.] ) ,
( [0.,0.,0.,1.,1.,1.], [0.,0.,0.,0.,0.,0.] ) ,
( [0.,0.,0.,0.,0.,0.], [0.,0.,0.,1.,1.,1.] ) ,
],
"groups":
( [0,1,2], [3,4,5] )
from jitcdde import t, y, jitcdde from symengine import sin import numpy as np T = 200 A = 0.9/2/np.pi τ_0 = 1.50 f = lambda z: 4*z*(1-z) τ = τ_0 + A*sin(2*np.pi*t) model = [ T*( -y(0) + f(y(0,t-τ)) ) ] DDE = jitcdde(model,max_delay=τ_0+A) DDE.past_from_function([0.4+0.2*sin(t)]) DDE.set_integration_parameters(max_step=0.01,first_step=0.01) DDE.integrate_blindly(τ_0+A,0.01) for time in DDE.t + 100 + np.arange(0,10,0.01): print(DDE.integrate(time)[0])
f_of_y0 = np.array([ 0.0045396904008868, 0.00002265673, 0.0043665702488807, 0.000328463955 ]) a = -0.025794 b1 = 0.0065 b2 = 0.0135 c = 0.02 k = 0.128 f = [ y(0) * ( a-y(0) ) * ( y(0)-1.0 ) - y(1) + k * (y(2) - y(0)), b1*y(0) - c*y(1), y(2) * ( a-y(2) ) * ( y(2)-1.0 ) - y(3) + k * (y(0) - y(2)), b2*y(2) - c*y(3) ] class basic_test(unittest.TestCase): @classmethod def setUpClass(self): self.ODE = jitcdde(f) def setUp(self): self.ODE.purge_past() self.ODE.add_past_point(-1.0, y0, f_of_y0) self.ODE.add_past_point( 0.0, y0, f_of_y0)
from jitcdde import t, y, jitcdde
import numpy as np
ω = np.random.normal(0.89, 0.0089, 2)
k = 0.25
delay = 4.5
f = [
ω[0] * (-y(1) - y(2)),
ω[0] * (y(0) + 0.165 * y(1)),
ω[0] * (0.2 + y(2) * (y(0) - 10.0)),
ω[1] * (-y(4) - y(5)) + k * (y(0,t-delay) - y(3)),
ω[1] * (y(3) + 0.165 * y(4)),
ω[1] * (0.2 + y(5) * (y(3) - 10.0))
]
DDE = jitcdde(f)
start_state = np.random.uniform(-0.5,0.5,6)
DDE.add_past_point(-delay, start_state, np.zeros(6))
DDE.add_past_point(0.0 , start_state, np.zeros(6))
DDE.step_on_discontinuities()
times = np.arange(DDE.t,DDE.t+1000,0.1)
data = np.vstack(DDE.integrate(T) for T in times)
np.savetxt("two_roesslers.dat", data)
def display_endemic_progress():
"""Display how a typical endemic progresses in time"""
beta = 0.000001
k = 6
gamma = 0.0002
delta = 0.3
# pylint: disable=invalid-name
mu = 0.1
d_one = 0.005
d_two = 0.001
tau = 5
initially_susceptible = 99980
initially_infected = 20
list_of_odes = [
gamma * y(4) - beta * k * y(0) * y(2),
beta * k * y(0) * y(2) - beta * k * y(0, t - tau) * y(2, t - tau),
beta * k * y(0, t - tau) * y(2, t - tau) - d_one * y(2) - delta * y(2),
delta * y(2) - d_two * y(3) - mu * y(3), mu * y(3) - gamma * y(4)
]
delayed_differential_equation = jitcdde(list_of_odes)
delayed_differential_equation.add_past_point(
-10.0, [initially_susceptible, 0, initially_infected, 0, 0],
[0, 0, 0, 0, 0])
delayed_differential_equation.add_past_point(
0, [initially_susceptible, 0, initially_infected, 0, 0],
[0, 0, 0, 0, 0])
delayed_differential_equation.step_on_discontinuities()
stoptime = 180
numpoints = 18000
times = delayed_differential_equation.t + \
np.linspace(1, stoptime, numpoints)
data = []
for time in times:
data.append(delayed_differential_equation.integrate(time))
npdata = np.array(data)
susceptible = npdata[:, 0]
exposed = npdata[:, 1]
infected = npdata[:, 2]
quarantined = npdata[:, 3]
recovered = npdata[:, 4]
fig = plt.figure()
subplot = fig.add_subplot(1, 1, 1)
subplot.plot(times, susceptible, label='Susceptible people')
subplot.plot(times, exposed, '-', label='Exposed people')
subplot.plot(times, infected, '--', label='Infected people')
subplot.plot(times, quarantined, '-.', label='Quarantined people')
subplot.plot(times, recovered, ':', label='Recovered people')
subplot.set_xlabel('Days from outbreak')
subplot.set_ylabel('Population')
subplot.legend(loc='best')
plt.savefig('all_compartments.svg', format="svg", dpi=1200)
def f(): yield omega[0] * (-y(1) - y(2)) yield omega[0] * (y(0) + 0.165 * y(1)) yield omega[0] * (0.2 + y(2) * (y(0) - 10.0)) yield omega[1] * (-y(4) - y(5)) + k * (y(0,t-delay) - y(3)) yield omega[1] * (y(3) + 0.165 * y(4)) yield omega[1] * (0.2 + y(5) * (y(3) - 10.0)) yield 0 yield 0
def test_check_index_too_high(self): DDE = jitcdde([y(1)]) with self.assertRaises(ValueError): DDE.check()
def setUp(self): double_mackey_glass = [ .25*y(0,t-15) / (1+y(0,t-15)**10) - 0.1*y(0), .25*y(1,t-15) / (1+y(1,t-15)**10) - 0.1*y(1) ] self.DDE = jitcdde(double_mackey_glass)
def test_check_index_negative(self): DDE = jitcdde([y(-1)]) with self.assertRaises(ValueError): DDE.check()
def test_dynamic_dependent_delay(self): g = lambda: [y(0,t-y(0))] with self.assertRaises(ValueError): _find_max_delay(_get_delays(g))
def test_time_dependent_delay(self): g = lambda: [y(0,2*t)] with self.assertRaises(ValueError): _find_max_delay(_get_delays(g))
def f_generator(): yield omega[0] * (-y(1) - y(2)) yield omega[0] * (y(0) + 0.165 * y(1)) yield omega[0] * (0.2 + y(2) * (y(0) - 10.0)) yield omega[1] * (-y(4) - y(5)) + 0.25 * (y(0,t-delay) - y(3)) yield omega[1] * (y(3) + 0.165 * y(4)) yield omega[1] * (0.2 + y(5) * (y(3) - 10.0))
import symengine
import numpy as np
from numpy.testing import assert_allclose
import unittest
if platform.system() == "Windows":
compile_args = None
else:
from jitcxde_common import DEFAULT_COMPILE_ARGS
compile_args = DEFAULT_COMPILE_ARGS+["-g","-UNDEBUG"]
omega = np.array([0.88167179, 0.87768425])
delay = 4.5
f = [
omega[0] * (-y(1) - y(2)),
omega[0] * (y(0) + 0.165 * y(1)),
omega[0] * (0.2 + y(2) * (y(0) - 10.0)),
omega[1] * (-y(4) - y(5)) + 0.25 * (y(0,t-delay) - y(3)),
omega[1] * (y(3) + 0.165 * y(4)),
omega[1] * (0.2 + y(5) * (y(3) - 10.0))
]
def get_past_points():
data = np.loadtxt("two_Roessler_past.dat")
for point in data:
yield (point[0], np.array(point[1:7]), np.array(point[7:13]))
y_10_ref = np.loadtxt("two_Roessler_y10.dat")
T = 10