#Se precentan los codigos que se usaron para obtener los diferentes graficos e imagenes.

#Pregunta 1

import matplotlib.pyplot as plt
from numpy import arange

alpha = 0.5471
beta = 0.0481
gamma = 0.001
def f(x,t): return alpha*x - beta*x*t - gamma*x**2

a, b = 0.0, 60.0
N = 1000
h = 0.0001
x = 1.0

tpoints = arange(a, b, h)
rk4_xpoints = []

for t in tpoints:
    rk4_xpoints.append(x)
    k1 = h*f(x, t)
    k2 = h*f(x+0.5*k1, t+0.5*h)
    k3 = h*f(x+0.5*k2, t+0.5*h)
    k4 = h*f(x+k3, t+h)
    x += (k1+2*k2+2*k3+k4)/6.0

plt.plot(tpoints, rk4_xpoints, label="RK4 depredador")
plt.xlabel("$t$")
plt.ylabel("$x(t)$")
plt.legend()
plt.show()

delta = 0.0466
epsilon = 0.8439
zeta = 0.001
def f(x,t): return delta*t*x - epsilon*x - zeta*x**2

a, b = 0.0, 60.0
N = 1000
h = 0.0001
x = 1.0

tpoints = arange(a, b, h)
rk4_xpoints = []

for t in tpoints:
    rk4_xpoints.append(x)
    k1 = h*f(x, t)
    k2 = h*f(x+0.5*k1, t+0.5*h)
    k3 = h*f(x+0.5*k2, t+0.5*h)
    k4 = h*f(x+k3, t+h)
    x += (k1+2*k2+2*k3+k4)/6.0

plt.plot(tpoints, rk4_xpoints, label="RK4 presa")
plt.xlabel("$t$")
plt.ylabel("$x(t)$")
plt.legend()
plt.show()

alpha = 0.5471
beta = 0.0481
gamma = 0.001
def f(x,t): return alpha*x - beta*x*t - gamma*x**2

a, b = 0.0, 20.0
N = 1000
h = 0.0001
x = 60.0

tpoints = arange(a, b, h)
rk4_xpoints = []

for t in tpoints:
    rk4_xpoints.append(x)
    k1 = h*f(x, t)
    k2 = h*f(x+0.5*k1, t+0.5*h)
    k3 = h*f(x+0.5*k2, t+0.5*h)
    k4 = h*f(x+k3, t+h)
    x += (k1+2*k2+2*k3+k4)/6.0
    
delta = 0.0466
epsilon = 0.8439
zeta = 0.001
def g(y,t): return delta*t*y - epsilon*y - zeta*y**2

a, b = 0.0, 20.0
N = 1000
h = 0.0001
y = 60.0

tpoints = arange(a, b, h)
rk4_ypoints = []

for t in tpoints:
    rk4_ypoints.append(y)
    k1 = h*g(y, t)
    k2 = h*g(y+0.5*k1, t+0.5*h)
    k3 = h*g(y+0.5*k2, t+0.5*h)
    k4 = h*g(y+k3, t+h)
    y += (k1+2*k2+2*k3+k4)/6.0
    
plt.plot(tpoints, rk4_xpoints, label="RK4 depredador")
plt.xlabel("$x(t)$")
plt.ylabel("$t$")
plt.plot(tpoints, rk4_ypoints, label="RK4 presa")
plt.xlabel("$t$")
plt.ylabel("$y(t)$")
plt.legend()
plt.show()

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import integrate
import ipywidgets as ipw

alpha = 0.5471
beta = 0.0481
gamma = 0.001
delta = 0.0466
epsilon = 0.8439
zeta = 0.001
x0 = 10
y0 = 5

def derivative(X, t, alpha, beta, gamma, delta, epsilon, zeta):
    x, y = X
    dotx = alpha*x - beta*x*y - gamma*x**2
    doty = delta*x*y - epsilon*y - zeta*y**2
    return np.array([dotx, doty])

Nt = 1000
tmax = 30
t = np.linspace(0.,tmax, Nt)
X0 = [x0, y0]
res = integrate.odeint(derivative, X0, t, args = (alpha, beta, gamma, delta, epsilon, zeta))
x, y = res.T

plt.figure()
plt.grid()
plt.title("odeint method")
plt.plot(t, x, 'xb', label = 'Depredadores')
plt.plot(t, y, '+r', label = "Presas")
plt.xlabel('Time t, [days]')
plt.ylabel('Population')
plt.legend()

plt.show()

#Pregunta 2

import matplotlib.pyplot as plt
import numpy as np

#Mandelbrot
def interate(x, y):
    C = complex(x, y)
    zp = complex(0, 0)
    for k in range(500):
        zp = zp**14 + C
        if abs(zp) > 2.5:
            return k+1
    return 500

N = 500

u = np.linspace(-2.5, 2.5, N)
v = np.linspace(-2.5, 2.5, N)

M = np.zeros((N, N))

print(u)
print(M)

for i in range(N):
    for j in range(N):
        M[i][j] = interate(u[i], v[j])

print(M)

plt.imshow(M)
plt.show()

#Mandelbar
def interate(x, y):
    C = complex(x, y)
    zp = complex(0, 0)
    for k in range(500):
        zp = zp.conjugate()**14 + C
        if abs(zp) > 2.5:
            return k+1
    return 500

N = 500

u = np.linspace(-2.5, 2.5, N)
v = np.linspace(-2.5, 2.5, N)

M = np.zeros((N, N))

print(u)
print(M)

for i in range(N):
    for j in range(N):
        M[i][j] = interate(u[i], v[j])

print(M.conjugate())

plt.imshow(M.conjugate())
plt.show()
plt.show()

#Pregunta 3

import numpy as np
import matplotlib.pyplot as plt


def Roessler(x, y, z, a=0.1, b=0.1, c=14):
    
    x_dot = -y - z
    y_dot = x + a*y
    z_dot = b + z*(x - c)
    return x_dot, y_dot, z_dot

dt = 0.01
num_steps = 10000

xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)

xs[0], ys[0], zs[0] = (0., 2., 1.)

for i in range(num_steps):
    x_dot, y_dot, z_dot = Roessler(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

    
ax = plt.figure().add_subplot(projection='3d')

ax.plot(xs, ys, zs, lw=1.)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_title("Roessler")

plt.show()

def Roessler(x, y, z, a=0.1, b=0.1, c=14):
    
    x_dot = -y - z
    y_dot = x + a*y
    z_dot = 0
    return x_dot, y_dot, z_dot

dt = 0.01
num_steps = 10000

xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)

xs[0], ys[0], zs[0] = (1., 2., 1)

for i in range(num_steps):
    x_dot, y_dot, z_dot = Roessler(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

    
ax = plt.figure().add_subplot(projection='3d')

ax.plot(xs, ys, zs, lw=1.)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_title("Roessler")

plt.show()

def Roessler(x, y, z, a=0.1, b=0.1, c=14):
    
    x_dot = -y - z
    y_dot = 0
    z_dot = b + z*(x - c)
    return x_dot, y_dot, z_dot

dt = 0.01
num_steps = 10000

xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)

xs[0], ys[0], zs[0] = (1., 2., 1)

for i in range(num_steps):
    x_dot, y_dot, z_dot = Roessler(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

    
ax = plt.figure().add_subplot(projection='3d')

ax.plot(xs, ys, zs, lw=1.)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_title("Roessler")

plt.show()

def Roessler(x, y, z, a=0.1, b=0.1, c=14):
    
    x_dot = 0
    y_dot = x + a*y
    z_dot = b + z*(x - c)
    return x_dot, y_dot, z_dot

dt = 0.01
num_steps = 10000

xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)

xs[0], ys[0], zs[0] = (1., 2., 1)

for i in range(num_steps):
    x_dot, y_dot, z_dot = Roessler(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

    
ax = plt.figure().add_subplot(projection='3d')

ax.plot(xs, ys, zs, lw=1.)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_title("Roessler")

plt.show()

from tqdm import tqdm
import matplotlib.pyplot as plt
import numpy as np


def LogisticMap():
    mu = np.arange(0, 2, 0.0001)
    a = 0.1
    c = 14
    y = 0.2
    z = 0.1
    x = 0.5
    iters = 1000
    last = 100
    for i in tqdm(range(iters+last)):
        x = -(x + a*y) - (mu + z*(x - c))
        if i >= iters:
            plt.plot(mu, x, ',k', alpha=0.25)
    plt.show()


LogisticMap()

def LogisticMap():
    mu = np.arange(0, 2, 0.0001)
    a = 0.1
    c = 14
    y = 0.2
    z = 0.1
    x = 1.
    iters = 1000
    last = 100
    for i in tqdm(range(iters+last)):
        x = -(x + a*y) - (mu + z*(x - c))
        if i >= iters:
            plt.plot(mu, x, ',k', alpha=0.25)
    plt.show()


LogisticMap()

def LogisticMap():
    mu = np.arange(0, 2, 0.0001)
    a = 0.1
    c = 14
    y = 0.2
    z = 0.1
    x = 5.0
    iters = 1000
    last = 100
    for i in tqdm(range(iters+last)):
        x = -(x + a*y) - (mu + z*(x - c))
        if i >= iters:
            plt.plot(mu, x, ',k', alpha=0.25)
    plt.show()


LogisticMap()