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dynamics.py
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dynamics.py
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import numpy as np
class vecField:
def __init__(self,system="Rober"):
self.system = system
if self.system=="Rober":
self.k1 = 0.04
self.k2 = 3e7
self.k3 = 1e4
self.dt_fine = 0.
elif self.system=="SIR":
self.beta = 0.1
self.gamma = 0.1
self.N = 1.
self.dt_fine = 0.
elif self.system=="Brusselator":
self.A = 1.
self.B = 3.
self.dt_fine = 0.
elif self.system=="Arenstorf":
self.a = 0.012277471
self.b = 1.-self.a
self.dt_fine = 0.
elif self.system=="Lorenz":
self.sigma = 10.
self.r = 28.
self.b = 8/3
self.dt_fine = 0.
elif self.system=="Burger":
self.nu = 1/50
self.L = 1.
self.N = 51
self.x = np.linspace(0,self.L,self.N)
self.dx = self.x[1]-self.x[0]
self.dt_fine = 0.
else:
print("This dynamics is not implemented.")
def eval(self,y):
if self.system=="Rober":
if len(y.shape)==2:
y1,y2,y3 = y[:,0:1],y[:,1:2],y[:,2:3]
return np.concatenate([
-self.k1*y1 + self.k3*y2*y3,
self.k1*y1 - self.k2*(y2**2) - self.k3*y2*y3,
self.k2*(y2**2)
],axis=1)
else:
y1,y2,y3 = y[0],y[1],y[2]
return np.array([
-self.k1*y1 + self.k3*y2*y3,
self.k1*y1 - self.k2*(y2**2) - self.k3*y2*y3,
self.k2*(y2**2)
])
elif self.system=="SIR":
if len(y.shape)==2:
y1,y2,y3 = y[:,0:1],y[:,1:2],y[:,2:3]
return np.concatenate((
-self.beta*y2*y1/self.N,
self.beta*y1*y2/self.N - self.gamma*y2,
self.gamma*y2
),axis=1)
else:
y1,y2,y3 = y[0],y[1],y[2]
return np.array([
-self.beta*y2*y1/self.N,
self.beta*y1*y2/self.N - self.gamma*y2,
self.gamma*y2
])
elif self.system=="Brusselator":
if len(y.shape)==2:
xx,yy = y[:,0:1],y[:,1:2]
return np.concatenate((
self.A+xx**2*yy - (self.B+1)*xx,
self.B*xx-xx**2*yy
),axis=1)
else:
xx,yy = y[0],y[1]
return np.array([
self.A+xx**2*yy - (self.B+1)*xx,
self.B*xx-xx**2*yy
])
elif self.system=="Arenstorf":
if len(y.shape)==2:
xx,xxp,yy,yyp = y[:,0:1],y[:,1:2],y[:,2:3],y[:,3:4]
D1 = ((xx+self.a)**2+yy**2)**(3/2)
D2 = ((xx-self.b)**2+yy**2)**(3/2)
return np.concatenate((
xxp,
xx+2*yyp-self.b*(xx+self.a)/D1-self.a*(xx-self.b)/D2,
yyp,
yy-2*xxp-self.b*yy/D1-self.a*yy/D2
),axis=1)
else:
xx,xxp,yy,yyp = y[0],y[1],y[2],y[3]
D1 = ((xx+self.a)**2+yy**2)**(3/2)
D2 = ((xx-self.b)**2+yy**2)**(3/2)
return np.array([
xxp,
xx+2*yyp-self.b*(xx+self.a)/D1-self.a*(xx-self.b)/D2,
yyp,
yy-2*xxp-self.b*yy/D1-self.a*yy/D2
])
elif self.system=="Lorenz":
if len(y.shape)==2:
xx,yy,zz = y[:,0:1],y[:,1:2],y[:,2:3]
return np.concatenate((
-self.sigma*xx+self.sigma*yy,
-xx*zz+self.r*xx-yy,
xx*yy-self.b*zz
),axis=1)
else:
xx,yy,zz = y[0],y[1],y[2]
return np.array([
-self.sigma*xx+self.sigma*yy,
-xx*zz+self.r*xx-yy,
xx*yy-self.b*zz
])
elif self.system=="Burger":
if len(y.shape)==2:
N = self.N
dx = self.dx
vv = np.ones(N-1)
Shift_forward = np.diag(vv,k=1)
Shift_backward = np.diag(vv,k=-1)
#For the boundary conditions
Shift_backward[-1]*=0
Shift_forward[0]*=0
D2 = (Shift_forward + Shift_backward - 2*np.eye(N))/(dx**2)
D1 = 1/(2*dx) * (Shift_forward-Shift_backward)
vec = -y * (y@D1.T) + self.nu * (y@D2.T)
return vec
else:
N = self.N
dx = self.dx
vv = np.ones(N-1)
Shift_forward = np.diag(vv,k=1)
Shift_backward = np.diag(vv,k=-1)
#For the boundary conditions
Shift_backward[-1]*=0
Shift_forward[0]*=0
D2 = (Shift_forward + Shift_backward - 2*np.eye(N))/(dx**2)
D1 = 1/(2*dx) * (Shift_forward-Shift_backward)
vec = -y * (D1@y) + self.nu * (D2@y)
return vec
else:
pass