from normal_forms import normal_form
import sympy
import numpy as np
from for_plotting import before_and_after
# Guckenheimer, Excercise 3.4.5
def f(x, y, mu=0):
f1 = y
f2 = -mu * y - x + x * x * x
return f1, f2
h = normal_form(f, (0, 0), 3)
before_and_after(f, h, -2, 2, -2, 2)
},
parnames={
1: 'p1',
2: 'p2',
3: 'p3'
},
U={
'x': 0,
'y': 0
},
PAR={
'p1': 0,
'p2': 8,
'p3': 3
},
ICP=['p2'],
RL1=14)
ab = auto.run(start('EP2'), c='ab.2')
ab = auto.rl(ab)
auto.sv(ab, 'ab')
auto.cl()
hb = ab('HB1')
p = hb['p1'], hb['p2'], hb['p3']
x = hb['x'][0], hb['y'][0]
h = normal_form(f, x, 3, p)
from normal_forms import normal_form
import sympy
# Murdock, Normal Forms and Unfoldings of Local Dynamical Systems, Example 4.5.24
def f(x, y, z):
f1 = 6 * x + x**2 + x * y + x * z + y**2 + y * z + z**2
f2 = 2 * y + x**2 + x * y + x * z + y**2 + y * z + z**2
f3 = 3 * z + x**2 + x * y + x * z + y**2 + y * z + z**2
return f1, f2, f3
h = normal_form(f, (0, 0, 0), 2)
# coeff of z**2
print h.fun[0].coeff(h.jet.var[2]**2)
import sympy f = lambda x, r=0: r + 1 - x - sympy.exp(-x) from normal_forms import normal_form h = normal_form(f, x=0, k=2) print h.fun print h(2)