File:Lorenz map for the Rossler attractor.png
Lorenz_map_for_the_Rossler_attractor.png (690 × 553 pixels, file size: 29 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionLorenz map for the Rossler attractor.png |
English: A replication of Figure 13 of Chaos in biological systems
LF Olsen, H Degn - Quarterly reviews of biophysics, 1985 Reproduced and discussed in Strogatz Nonlinear Dynamics (2nd edition), Figure 10.6.7 ```python import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp def rossler_system(t, xyz, a, b, c): x, y, z = xyz dx_dt = -y - z dy_dt = x + a * y dz_dt = b + z * (x - c) return [dx_dt, dy_dt, dz_dt]
a = 0.2 b = 0.2 c = 5
xyz0 = [1.0, 1.0, 1.0] tmin, tmax = 0, 10000 t_span = [tmin, tmax] t_eval = np.linspace(t_span[0], t_span[1], (tmax-tmin) * t_resolution) solution = solve_ivp(rossler_system, t_span, xyz0, args=(a, b, c), t_eval=t_eval) x, y, z = solution.y def find_local_maxima(arr): local_maxima = [] for i in range(1, len(arr) - 1): if arr[i - 1] < arr[i] > arr[i + 1]: local_maxima.append(arr[i]) return local_maxima local_maxima = find_local_maxima(x) x = local_maxima[10:-1] y = local_maxima[11:] z = np.polyfit(x, y, 5) p = np.poly1d(z) fig, ax = plt.subplots(figsize=(8, 6)) ax.scatter(local_maxima[10:-1], local_maxima[11:], s=0.01) ax.plot(sorted(x), p(sorted(x)), color='red', linewidth=0.2) ax.set_xlabel("$x_{max}(n)$") ax.set_ylabel("$x_{max}(n+1)$") ax.set_title(f"Lorenz map for the Rössler attractor, with $a={a}, b={b}, c={c}$") plt.show() ``` |
Date | |
Source | Own work |
Author | Cosmia Nebula |
Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:50, 18 April 2023 | 690 × 553 (29 KB) | Cosmia Nebula (talk | contribs) | c = 5 | |
22:35, 18 April 2023 | 587 × 460 (25 KB) | Cosmia Nebula (talk | contribs) | Uploaded while editing "Rössler attractor" on en.wikipedia.org |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on el.wikipedia.org
- Usage on en.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Software used | |
---|---|
Horizontal resolution | 39.37 dpc |
Vertical resolution | 39.37 dpc |