File:Van der Pol oscillator phase plot 01.webm
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Van_der_Pol_oscillator_phase_plot_01.webm (file size: 22.56 MB, MIME type: video/webm)
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Summary
DescriptionVan der Pol oscillator phase plot 01.webm |
English: ```python
%%capture for i, mu in enumerate(np.exp(np.linspace(np.log(0.1), np.log(3.0), 121))): def system(t, xy): x, y = xy dx = y dy = mu * (1-x**2) * y - x return [dx, dy] vmin, vmax, wmin, wmax = -4, 4, -4, 4 t_span = [0, 10] trajectory_resolution = 30 initial_conditions = [(x, y) for x in np.linspace(vmin, vmax, trajectory_resolution) for y in np.linspace(wmin, wmax, trajectory_resolution)] sols = {} for ic in initial_conditions: sols[ic] = solve_ivp(system, t_span, ic, dense_output=True, max_step=0.01) vs = np.linspace(vmin, vmax, 200) v_axis = np.linspace(vmin, vmax, 20) w_axis = np.linspace(wmin, wmax, 20) v_values, w_values = np.meshgrid(v_axis, w_axis) dv, dw = system(0, (v_values, w_values)) fig, ax = plt.subplots(figsize=(16,16)) # integral curves for ic in initial_conditions: sol = sols[ic] ax.plot(sol.y[0], sol.y[1], color='k', alpha=0.4, linewidth=0.5) # vector fields arrow_lengths = np.sqrt(dv**2 + dw**2) dv = dv / arrow_lengths * np.tanh(arrow_lengths) dw = dw / arrow_lengths * np.tanh(arrow_lengths) alpha_values = 1 - (arrow_lengths / np.max(arrow_lengths))**0.2 ax.quiver(v_values, w_values, dv, dw, color='blue', linewidth=0.5, scale=25, alpha=alpha_values) # nullclines vs = np.linspace(-0.99, 0.99, 1000) ax.plot(vs, vs/(1-vs**2)/mu, color="green", alpha=0.4) vs = np.linspace(vmin, -1.01, 1000) ax.plot(vs, vs/(1-vs**2)/mu, color="green", alpha=0.4) vs = np.linspace(1.01, vmax, 1000) ax.plot(vs, vs/(1-vs**2)/mu, color="green", alpha=0.4) ax.set_title(f'van der Pol oscillator\n$\mu={mu:.2f}$') ax.set_xlim(vmin, vmax) ax.set_ylim(wmin, wmax) ax.set_xticks([]) ax.set_yticks([]) dir_path = f"./vdp" if not os.path.exists(dir_path): os.makedirs(dir_path) fig.savefig(f"{dir_path}/{i}.png") import imageio.v3 as iio import os from natsort import natsorted import moviepy.editor as mp for dir_path in ["./vdp", "./vdp2"]: file_names = natsorted((fn for fn in os.listdir(dir_path) if fn.endswith('.png'))) # Create a list of image files and set the frame rate images = [] fps = 12 # Iterate over the file names and append the images to the list for file_name in file_names: file_path = os.path.join(dir_path, file_name) images.append(iio.imread(file_path)) filename = dir_path[2:] iio.imwrite(f"{filename}.gif", images, duration=1000/fps, rewind=True) clip = mp.ImageSequenceClip(images, fps=fps) clip.write_videofile(f"{filename}.mp4")``` |
Date | |
Source | Own work |
Author | Cosmia Nebula |
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Date/Time | Dimensions | User | Comment | |
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current | 04:23, 22 April 2023 | (22.56 MB) | imagescommonswiki>Cosmia Nebula | correct parametrization this time |
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