PyDSTool集成步骤

Question

我有一个ODE系统。我正在寻找使用PyDSTool的系统解决方案。我尝试进行集成步骤，但是我收到了错误。

pgadmin4

通过下一行我得到一个错误：

import PyDSTool as ds
from PyDSTool import Par, Var
import time
from PyDSTool import *

# Declare names and initial values for (symbolic) parameters
varepsilon = pow(10, -2)
j = 2.5*pow(10, -5)
e = 3.0

y8 = lambda y1,y5,y7: 1 / (1 - 2 / y1) * math.sqrt(y5 ** 2 + (1 - 2 / y1) * (1 + y1 ** 2 * y7 ** 2))
E0 = lambda y1,y8: (1 - 2 / y1) * y8
Phi0 = lambda y1,y7: y1 ** 2 * y7

# Compute nontrivial boundary equilibrium initial condition from parameters (see reference for derivation)
u0 = -math.sqrt(-1 + math.sqrt(varepsilon ** 2 + 12) / varepsilon) * math.sqrt(2) / 6
v0 = 1 / (1 - 2 / e) * math.sqrt(j ** 2 + (1 - 2 / e) * (e ** 2 * u0 ** 2 + 1))

y08 = y8(y1=e, y5=j, y7=u0);
E = E0(y1=e, y8=y08); Phi = Phi0(y1=e, y7=u0)

z01, z03, z04, z05, z07, z08 = e, 0.0, 0.0, j, u0, v0
# Declare symbolic variables
z1, z3, z4, z5, z7, z8 = Var('z1'), Var('z3'), Var('z4'), Var('z5'), Var('z7'), Var('z8')

# Create Symbolic Quantity objects for definitions
p1 = -z1*z5/(z1 - 2);
p3 = -z1**2 *z7;
p4 = z8*(1 - 2/z1);
Q1 = -z5**2/(z1*(z1 - 2)) + (z8**2/z1**3 - z7**2)*(z1 - 2);
Q3 = 2*z5*z7/z1;
Q4 = 2*z5*z8/(z1*(z1 - 2));
c1 = z1*z7*varepsilon;
c3 = -z1*z5*varepsilon;
C = z7*varepsilon/z1 - z8*(1 - 2/z1);
d1 = -z1*z8*varepsilon;
d3 = z1*z5*varepsilon;
B = z1**2*z7 - z8*varepsilon*(1 - 2/z1);
Omega = 1/(c1*d3*p3+c3*d1*p4-c3*d3*p1);

# differential equations
z1dot = z5;
z3dot  = z7;

z4dot  = z8;
z5dot  = Omega*(-Q1*c1*d3*p3 - Q1*c3*d1*p4 + Q1*c3*d3*p1 + B*c3*p4 + C*d3*p3 + E*d3*p3 - Phi*c3*p4);
z7dot  = -Omega*(Q3*c1*d3*p3 + Q3*c3*d1*p4 - Q3*c3*d3*p1 + B*c1*p4 - C*d1*p4 + C*d3*p1 - E*d1*p4 + E*d3*p1 - Phi*c1*p4);
z8dot = Omega*(-Q4*c1*d3*p3 - Q4*c3*d1*p4 + Q4*c3*d3*p1 + B*c1*p3 - B*c3*p1 - C*d1*p3 - E*d1*p3 - Phi*c1*p3 + Phi*c3*p1);

# Build Generator
DSargs = args(name='Sining particle')
#print(dir(DSargs))
#DSargs.pars = [varepsilon, j, e]
DSargs.MaxNumPoints = 450
DSargs.MaxStepSize  = 2e-2
DSargs.MinStepSize  = 1e-5
DSargs.StepSize     = e-2
DSargs.tdata = [0.0, 0.1] 
DSargs.varspecs = args(z1=z1dot, z3=z3dot, z4=z4dot, z5=z5dot, z7=z7dot, z8=z8dot)
# Use eval method to get a float value from the symbolic definitions given in
# terms of parameter values
DSargs.ics = args(z1=z01, z3=z03, z4=z04, z5=z05, z7=z07, z8=z08)
ode = Generator.Vode_ODEsystem(DSargs)

t = time.time()
result = ode.compute('test')
print("time for integration: %f" %(time.time() - t))
pts = result.sample()

plt.plot(pts['t'], pts['z7'], label='x')
plt.legend()
plt.xlabel('t')
plt.show()

图书馆PyDSTool在互联网上几乎没有培训信息。 我做错了什么？以及如何正确确定整合步骤？