A simple GUI for Lotka Volterra equations

A demo of Lotka-Volterra equation solver. Initial conditions and parameters are set interactively.

• Features

  • Quib-linked widgets

  • Running user defined functions using q

  • Graphics quibs

  • Graphics-driven assignments

  • Inverse assignments

• Try me

  • Try dragging up and down the triangle markers to set the initial conditions.

  • Try adjusting the sliders to set equation parameters.

from pyquibbler import iquib, initialize_quibbler, q
initialize_quibbler()
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import numpy as np
from scipy.integrate import solve_ivp
%matplotlib tk

def solveLV(x0, pars, tfinal):
    a, b, c, d = pars

    def LV(t,v):
        # Lotka-Volterra equations:
        dv = np.zeros(np.shape(v))
        dv[0] =  a * v[0] - b * v[0] * v[1]
        dv[1] = -c * v[1] + d * v[0] * v[1]
        return dv

    return solve_ivp(LV, [0, tfinal], x0, rtol=1e-6)

# Initial condition:
x0 = iquib([2.0, 0.5])

# Parameters:
abcd = iquib([1., 1., 1., 1.])

# Final time:
tf = iquib(40)

# Define the ODE solver quib:
sol = q(solveLV, x0, abcd, tf)

y = sol['y']
t = sol['t']

# Prepare figure:
fig = plt.figure()
axs = fig.add_axes([0.15, 0.4, 0.8, 0.5])
axs.set_xlim([-2, tf])
mx = np.max([4., np.max(y)])
axs.set_ylim([0, mx])
axs.set_xlabel('time')
axs.set_ylabel('abundance')
axs.set_title('Lotka Volterra')

# Plot results:
axs.plot(t, y[0, :], 'r', linewidth=1)
axs.plot(t, y[1, :], 'b', linewidth=1)

# Plot initial conditions:
axs.plot(-1, x0[0], marker='>', markerfacecolor='r', markersize=16)
axs.plot(-1, x0[1], marker='>', markerfacecolor='b', markersize=16)
axs.plot([0, 0], [0, mx], 'k-', linewidth=0.5)

# Add legend:
ttls = iquib(['Rabbits', 'Foxes']);
axs.legend(ttls, fontsize=14, loc='upper right')

# Set sliders for parameters:
params_labels = iquib(['growth', 'killing', 'death', 'preying']);
for i in range(4):
    slider_axs = fig.add_axes([0.3, 0.2 - i*0.04, 0.5, 0.02])
    Slider(ax=slider_axs, label=params_labels[i],
           valmin=0, valmax=4, valstep=0.1, valinit=abcd[i])