CoCalc -- Notebook in R.ipynb

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ubuntu2204

Kernel: Python 3 (system-wide)

In [0]:

In [6]:

import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint

# Lotka-Volterra (predator-prey) model
def model(z, t):
    x = z[0] # Prey population
    y = z[1] # Predator population
    dxdt = alpha*x - beta*x*y # change in prey population
    dydt = delta*x*y - gamma*y # change in predator population
    dzdt = [dxdt,dydt]
    return dzdt

# Initial conditions
z0 = [600, 400]

# Parameters
alpha = 1.1 # Prey birth rate
beta = 0.4  # Predator's efficiency in converting consumed prey into predator increments
gamma = 0.4 # Predator death rate
delta = 0.1 # Predator's ability to find and consume prey

# Time vector
t = np.linspace(0, 50, 100)

# Solve ODE
z = odeint(model, z0, t)

plt.figure(figsize=[8,5])
plt.plot(t, z[:, 0], 'b-', label='Prey population')
plt.plot(t, z[:, 1], 'r--', label='Predator population')
plt.xlabel('Time')
plt.ylabel('Population')
plt.tile('Lotka-Volterra Predator-Prey Model')
plt.grid()
plt.legend()
plt.show()

Out[6]:

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
/tmp/ipykernel_48970/3244130731.py in <cell line: 34>()
     32 plt.xlabel('Time')
     33 plt.ylabel('Population')
---> 34 plt.tile('Lotka-Volterra Predator-Prey Model')
     35 plt.grid()
     36 plt.legend()
AttributeError: module 'matplotlib.pyplot' has no attribute 'tile'

In [4]:

from sympy import *
from sympy.abc import a, b, s, t, u, v, w, x, y, z
k, m, n = symbols("k, m, n", integer=True)
f, g, h = symbols("f, g, h", cls=Function)

In [5]:

dx0, dx1 = symbols("dx0, dx1")
Derivative.as_finite_difference(f(x).diff(x), [x-dx0, x, x+dx1])

Out[5]:

$\displaystyle \frac{dx_{0} f{\left(dx_{1} + x \right)}}{dx_{1} \left(dx_{0} + dx_{1}\right)} + \frac{\left(-1 + \frac{dx_{1}}{dx_{0}}\right) f{\left(x \right)}}{dx_{1}} - \frac{dx_{1} f{\left(- dx_{0} + x \right)}}{dx_{0} \left(dx_{0} + dx_{1}\right)}$

In [0]:

A=2

In [0]:

B=3

In [0]:

A+B

In [0]:

import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint

# Lotka-Volterra (predator-prey) model
def model(z, t):
    x = z[0] # Prey population
    y = z[1] # Predator population
    dxdt = alpha*x - beta*x*y # change in prey population
    dydt = delta*x*y - gamma*y # change in predator population
    dzdt = [dxdt,dydt]
    return dzdt

# Initial conditions
z0 = [600, 400]

# Parameters
alpha = 1.1 # Prey birth rate
beta = 0.4  # Predator's efficiency in converting consumed prey into predator increments
gamma = 0.4 # Predator death rate
delta = 0.1 # Predator's ability to find and consume prey

# Time vector
t = np.linspace(0, 50, 100)

# Solve ODE
z = odeint(model, z0, t)

plt.figure(figsize=[8,5])
plt.plot(t, z[:, 0], 'b-', label='Prey population')
plt.plot(t, z[:, 1], 'r--', label='Predator population')
plt.xlabel('Time')
plt.ylabel('Population')
plt.title('Lotka-Volterra Predator-Prey Model') # Fixed typo here
plt.grid()
plt.legend()
plt.show()

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