pycont-lite 0.1.0

Lightweight matrix-free pseudo-arclength continuation with bifurcation detection and branch switching.

PyCont

PyCont is a simple, matrix-free pseudo-arclength continuation library for solving parametric nonlinear systems of the form

$$ G(u, p) = 0 $$

with automatic detection of bifurcation points and branch switching. In particular, PyCont uses

• Matrix-free implementation through nonlinear Newton-Krylov solvers
• Precise bifurcation point localization (via bisection)
• Branch switching at bifurcation points
• Lightweight and easy to integrate into your workflows
• No derivatives or Jacobians needed! Everything works directly on the level of G(u, p).

Installation

pip install pycont

Minimal Working Example (Pitchfork Bifurcation)

import numpy as np
import pycont
import matplotlib.pyplot as plt

# Define the pitchfork function
def G(u, p):
    return u**3 - p*u

# Initial guess
u0 = np.array([1e-2])
p0 = 0.0

# Run continuation
continuation_result = pycont.pseudoArclengthContinuation(
    G,
    u0, p0,
    ds_min=0.001,
    ds_max=0.05,
    ds=0.01,
    N=200
)

# Plot the solution curve
for n in range(len(continuation_result.branches)):
		branch = continuation_result.branches[n]
		ax.plot(branch['p'], branch['u'], 'blue')
plt.xlabel('p')
plt.ylabel('u')
plt.title('Bifurcation diagram')
plt.grid()
plt.show()  

License

This project is licensed under the MIT License — see the LICENSE file for details.

Acknowledgement

I started this project because there are (in my opinion) no good, lightweight, and easy to use numerical continuation packages in the python ecosystem. These days, researchers are too often forced to use ancient Fortran packages like AUTO, or language-specific tools like MATCONT in Matlab. PyCont seeks to create an elegent package with all features for Python - the default language for scientific computing and machine learning.

If you want to see new features, either contact me or write a pull request. I will continue updating PyCont based on my own needs, and soon PyCont will include Hopf bifurcation detection and limit cycle detection. For questions or requests, feel free to contact me at hannesvdc[at]gmail[dot]com.