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pull_back.py
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pull_back.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Sep 24 12:47:14 2017
@author: jithin
A module of functions to study the Pullback attractor.
"""
import matplotlib.pyplot as plt
import numpy as np
def fwd_tractor(v,xspace,r,dt=0.005, limy = []):
"""
Plots the forward attractor governed by the function v
for the initial conditions in xspace for r steps of
size dt.
"""
for x_0 in xspace:
t=np.zeros(r)
x=np.zeros(r+1)
x[0]= x_0
for i in range(r):
t[i]=i*dt
x[i+1]=x[i]+dt*v(x[i],t[i])
plt.plot(t,x[:-1])
if limy != []:
plt.ylim(limy)
plt.xlabel('t')
plt.ylabel('x(t)')
plt.title('Forward attractor')
def pull_tractor(v,tspace,xspace,r,dt=0.005, limy = []):
"""
Plots the forward attractor governed by the function v
for the initial conditions in xspace for r steps of
size dt.
"""
for x_0 in xspace:
for t0 in tspace:
t=np.zeros(r)
x=np.zeros(r+1)
x[0]= x_0
for i in range(r):
t[i]=i*dt +t0
x[i+1]=x[i]+dt*v(x[i],t[i])
plt.plot(t,x[:-1])
if limy != []:
plt.ylim(limy)
plt.xlabel('t')
plt.ylabel('x(t)')
plt.title('Pullback attractor')