def solveDiamondRotatedInteralMult(init,T,dt=0.025,mu=4.0,beta=1.2,A=2.0,a=0.2,b=0.2,c=5.7,d=0.25,B=1.25):
times = np.arange(0,T,dt)
x = np.zeros((len(times),len(init)))
x[0,:] = init
for k,t in enumerate(times[:-1]):
x[k+1,:] = rk4.solverp(t,x[k,:],dt,diamondRotatedInternalMult,mu=mu,beta=beta,A=A,a=a,b=b,c=c,d=d,B=B)
return x
def solvePendulum(init,
T,
dt=0.05,
mu=4.0,
beta=2.0,
gamma=3.5,
delta=2.0,
A=2.0,
B=4.0,
C=1.0,
D=1.0):
times = np.arange(0, T, dt)
x = np.zeros((len(times), len(init)))
x[0, :] = init
for k, t in enumerate(times[:-1]):
x[k + 1, :] = rk4.solverp(t,
x[k, :],
dt,
triplePendulum,
mu=mu,
beta=beta,
gamma=gamma,
delta=delta,
A=A,
B=B,
C=C,
D=D)
return x
def solveRotatedRossler(init,T,dt=0.01,a=0.2,b=0.2,c=5.7):
times = np.arange(0,T,dt)
x = np.zeros((len(times),len(init)))
x[0,:] = init
for k,t in enumerate(times[:-1]):
x[k+1,:] = rk4.solverp(t,x[k,:],dt,rotatedRossler,a=a,b=b,c=c)
return x
def solveRotatedLorenz(init,finaltime,dt=0.025,sigma=10.,rho=28.,beta=8/3.):
'''
init = [x[0],y[0],z[0]] are the initial conditions
dt is the time step
last three args are Lorenz parameters
'''
times = np.arange(0,finaltime,dt)
timeseries = np.zeros((len(times),len(init)))
timeseries[0,:] = init
for k,ti in enumerate(times[:-1]):
timeseries[k+1,:] = rk4.solverp(ti,timeseries[k,:],dt,rotatedLorenz,sigma=sigma,rho=rho,beta=beta)
return timeseries
def solvePendulum(init, T, dt=0.1, mu=4.0, beta=1.2, A=2.0):
times = np.arange(0, T, dt)
x = np.zeros((len(times), len(init)))
x[0, :] = init
for k, t in enumerate(times[:-1]):
x[k + 1, :] = rk4.solverp(t,
x[k, :],
dt,
doublePendulum,
mu=mu,
beta=beta,
A=A)
return x
def solveDiamond(init, T, dt=0.1, mu=4.0, beta=2.0, A=2.0, gamma=10.0, B=1.25):
times = np.arange(0, T, dt)
x = np.zeros((len(times), len(init)))
x[0, :] = init
for k, t in enumerate(times[:-1]):
x[k + 1, :] = rk4.solverp(t,
x[k, :],
dt,
doublePendulumDiamond,
mu=mu,
beta=beta,
A=A,
gamma=gamma,
B=B)
return x
def solveCycle(init, finaltime, dt=0.1, a=2.0, b=2.0, c=2.0):
'''
init = [x[0],y[0],z[0]] are the initial conditions
dt is the time step
finaltime is the length of time to solve for
'''
times = np.arange(0, finaltime, dt)
timeseries = np.zeros((len(times), len(init)))
timeseries[0, :] = init
for k, ti in enumerate(times[:-1]):
timeseries[k + 1, :] = rk4.solverp(ti,
timeseries[k, :],
dt,
singlecycle,
a=a,
b=b,
c=c)
return timeseries
def solvePendulum(init,
T,
func=doublePendulumForm1,
dt=0.1,
mu=4.0,
beta=2.0,
A=2.0,
gamma=10.0):
times = np.arange(0, T, dt)
x = np.zeros((len(times), len(init)))
x[0, :] = init
for k, t in enumerate(times[:-1]):
x[k + 1, :] = rk4.solverp(t,
x[k, :],
dt,
func,
mu=mu,
beta=beta,
A=A,
gamma=gamma)
return x
def solvePredPrey(init,
finaltime,
dt=0.025,
odes=complotkavolterra4D,
kwargs={
'A': 1,
'B': 1,
'C': 1,
'D': 1
}):
'''
init = [x[0],y[0]] are the initial conditions
finaltime is length of simulation, dt is the time step
odes is the function handle to be integrated
kwargs dict contains parameters for odes function
'''
times = np.arange(0, finaltime, dt)
timeseries = np.zeros((len(times), len(init)))
timeseries[0, :] = init
for k, ti in enumerate(times[:-1]):
timeseries[k + 1, :] = rk4.solverp(ti, timeseries[k, :], dt, odes,
**kwargs)
return timeseries