Jump to content

File:Fitzhugh-nagumo b = 2.0, with stable and unstable manifolds marked.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (1,314 × 1,321 pixels, file size: 505 KB, MIME type: image/png)

Summary

Description
English: ```python

from matplotlib.widgets import AxesWidget import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp from scipy import optimize

for alpha in [0.09]:

 # Define the parameter values
 a = 0.7
 b = 2.0 # If b < 1.5, then there are stable loops. Else there are no loops.
 tau = 12.5
 R = 0.1
 I_ext_0 = (2/3 + (a-1)/b)/R
 I_ext_1 = (-2/3 + (a+1)/b)/R
 I_ext_min = min(I_ext_0, I_ext_1) - 2.0 / R
 I_ext_max = max(I_ext_0, I_ext_1) + 2.0 / R
 I_ext = I_ext_min * (alpha - 1.0)/(-2.0) + I_ext_max * (alpha + 1.0)/(+2.0)
 # If alpha < 1, then all trajectories fall to a stable equilibrium
 # If alpha > 1, and b < 1.5, then all trajectories fall to a stable loop.
 # Define the system of ODEs
 def system(t, y):
     v, w = y
     dv = v - (v ** 3) / 3 - w + R * I_ext
     dw = (1 / tau) * (v + a - b * w)
     return [dv, dw]
 def system_reversed(t, y):
     v, w = y
     dv = v - (v ** 3) / 3 - w + R * I_ext
     dw = (1 / tau) * (v + a - b * w)
     return [-dv, -dw]
 vmin, vmax, wmin, wmax = -2, 2, -2+R*I_ext, 2+R*I_ext
 t_span = [0, 100]
 trajectory_resolution = 10
 def fun(x):
   v = x[0]
   return v-v**3/3 + R * I_ext - (v+a)/b
 sol = optimize.root(fun, [0], method='hybr')
 x_root = sol.x[0]
 y_root = (x_root+a)/b
 # vmin, vmax, wmin, wmax = -1.5, -0.5, -1.1 +1/3 + R * I_ext, -0.8 +1/3 + R * I_ext
 # initial_conditions = [(-1.0, y) for y in np.linspace(-0.16, -0.03, 30)]
 initial_conditions = [(x, y) for x in np.linspace(vmin, vmax, trajectory_resolution) for y in np.linspace(wmin, wmax, trajectory_resolution)]
 epsilon = 0.005
 initial_conditions += [(x, y) for x in np.linspace(x_root - epsilon, x_root+epsilon, trajectory_resolution)  for y in np.linspace(y_root - epsilon, y_root+epsilon, trajectory_resolution)]
 sols = {}
 for ic in initial_conditions:
     sols[ic] = solve_ivp(system, t_span, ic, dense_output=True, max_step=0.1)
 sols_reversed = {}
 for ic in initial_conditions:
     sols_reversed[ic] = solve_ivp(system_reversed, t_span, ic, dense_output=True, max_step=0.1)
 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 = v_values - (v_values ** 3) / 3 - w_values + R * I_ext
 dw = (1 / tau) * (v_values + a - b * 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)
   sol = sols_reversed[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)
 alpha_values = 1 - (arrow_lengths / np.max(arrow_lengths))**0.4
 ax.quiver(v_values, w_values, dv, dw, color='blue', linewidth=0.5, scale=25, alpha=alpha_values)
 # nullclines
 ax.plot(vs, vs - vs**3/3 + R * I_ext,  color="green", alpha=0.4, label="v nullcline")
 ax.plot(vs, (vs + a) / b, color="red", alpha=0.4, label="w nullcline")
 # ax.set_xlabel('v')
 # ax.set_ylabel('w')
ax.set_title(f'FitzHugh-Nagumo Model\n$b={b:.2f}$\t\t$I_
Estremeñu: (missing text)
= {I_ext:.2f
})
 # ax.legend()
 ax.set_xlim(vmin, vmax)
 ax.set_ylim(wmin, wmax)
 # ax.set_xticks([])
 # ax.set_yticks([])
 plt.show()
```
Source Own work Edit this at Structured Data on Commons
Author

|date=2023-04-25 |source=Own work |author=Cosmia Nebula }}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current23:57, 25 April 2023Thumbnail for version as of 23:57, 25 April 20231,314 × 1,321 (505 KB)Cosmia NebulaUploaded while editing "FitzHugh–Nagumo model" on en.wikipedia.org

The following page uses this file:

Metadata