Created
June 23, 2022 15:12
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Van der pol oscillator
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import scipy as sc | |
import numpy as np | |
from scipy import integrate | |
from matplotlib import pyplot as plt | |
from matplotlib.ticker import (MultipleLocator, FormatStrFormatter, AutoMinorLocator, AutoLocator) | |
def osz(y, t, gamma1, gamma2, omega0): | |
x, p = y | |
dydt = [p, -(-gamma1 + gamma2 * x**2)*p - omega0**2 * x] | |
return dydt | |
def main(): | |
t = np.arange(0, 100, 0.01) | |
sol1 = sc.integrate.odeint(osz, y0=[0, 1], t=t, args=(1, 1, 1)) | |
sol2 = sc.integrate.odeint(osz, y0=[0, 1], t=t, args=(1, 1, 5)) | |
sol3 = sc.integrate.odeint(osz, y0=[0, 1], t=t, args=(1, 1, 1/5)) | |
fig, ax = plt.subplots(1, 1, figsize=(10, 7), dpi=100) | |
ax.xaxis.set_minor_locator(AutoMinorLocator()) | |
ax.xaxis.set_major_locator(AutoLocator()) | |
ax.yaxis.set_minor_locator(AutoMinorLocator()) | |
ax.yaxis.set_major_locator(AutoLocator()) | |
ax.tick_params(which='both', width=0.8) | |
ax.tick_params(which='major', length=7) | |
ax.tick_params(which='minor', length=4, grid_linestyle="--", grid_color="lightgray") | |
ax.grid(True, which="both") | |
ax.plot(sol1[:, 0], sol1[:, 1], label="$\gamma_1 / \omega_0 = 1$", linewidth=1) | |
ax.plot(sol2[:, 0], sol2[:, 1], label="$\gamma_1 / \omega_0 = 1/5$", linewidth=1) | |
ax.plot(sol3[:, 0], sol3[:, 1], label="$\gamma_1 / \omega_0 = 5$", linewidth=1) | |
ax.set_title("Van der Pol, $\gamma_1 = \gamma_2 = 1$") | |
ax.legend() | |
ax.set_xlabel("$x(t)$") | |
ax.set_ylabel("$p(t)$") | |
plt.show() | |
if __name__ == "__main__": | |
main() |
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