Example #1
0
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)
Example #2
0
                 },
                 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)
Example #3
0
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)