jaxcont 0.4.0

Differentiable continuation and bifurcation analysis in JAX.

JaxCont turns an equilibrium continuation sweep into a JAX program. Follow branches through folds with pseudo-arclength continuation, detect and refine fold/Hopf events, and compose the analysis with jax.jit, jax.vmap, and automatic differentiation.

📖 Read the full documentation

Why JaxCont?

• Transform the whole analysis. Batch ensembles of branches with vmap and differentiate bifurcation locations for inverse design.
• Stay on the branch. Adaptive pseudo-arclength continuation passes folds; natural continuation is available when the parameter remains regular.
• See and validate the result. Plot stability-aware bifurcation diagrams and eigenvalue trajectories with JaxCont events plus MatCont, BifurcationKit, or analytic reference markers.

The current surface supports equilibrium and periodic-orbit continuation, their principal codimension-one events, direct codimension-two point solvers, two-parameter continuation (fold/Hopf curves with their own codimension-two events), and infinitesimal phase response curves (iPRC, prc_curve, cross-validated against MatCont) plus their parameter-derivative sensitivity (dPRC, dprc_curve, validated independently -- MatCont does not compute this quantity). Branch switching and general connecting-orbit/BVP workflows remain future work.

_{JaxCont's branch (blue) traced independently over MatCont 7.6's reference (orange) — more cases, including known limitations, in the MatCont validation suite.}

Installation

JaxCont requires Python 3.11 or newer.

pip install jaxcont

See the JAX installation guide when selecting CPU, GPU, or TPU support.

Quick start

Continue u² + p = 0 through its fold at p = 0:

import jax.numpy as jnp
import matplotlib.pyplot as plt
import jaxcont as jc

def saddle_node(u, p, args):
    return u**2 + p

problem = jc.bif_problem(
    saddle_node,
    u0=jnp.array([1.0]),
    p0=-1.0,
    state_names=["u"],
    param_name="p",
)

result = jc.continuation(
    problem,
    p_span=(-1.0, 0.2),
    settings=jc.ContinuationPar(ds=0.03, max_steps=200),
    events=[jc.Fold()],
)

print([(event.kind, event.p) for event in result.events])
result.plot(annotate=True, title="Saddle-node bifurcation")
plt.show()

The same result can drive a stability-spectrum plot:

from jaxcont.viz import plot_eigenvalues

plot_eigenvalues(result, shade_stability=True)

Explore

• Documentation home
• Quickstart
• Example gallery
• example_03_van_der_pol.py — Hopf crossing with JaxCont and MatCont markers
• example_06_vmap_sweep.py — batched continuation with vmap
• example_07_differentiable.py — differentiable bifurcation analysis
• examples/MatCont — reproducible analytic, MATLAB/MatCont and JaxCont validation cases

Development

git clone https://github.com/Ziaeemehr/JaxCont.git
cd JaxCont
python -m pip install -e ".[dev]"
python -m pytest

Contributions are welcome; see CONTRIBUTING.md, the roadmap, and the MatCont validation suite.

Citation

If JaxCont supports your research, please cite the archived release. Full citation metadata (including both DOIs) is in CITATION.cff -- GitHub renders a "Cite this repository" button from it automatically.

@software{ziaeemehr_jaxcont_2026,
  author  = {Ziaeemehr, Abolfazl},
  title   = {JaxCont: Differentiable Continuation and Bifurcation Analysis in JAX},
  year    = {2026},
  version = {0.3.1},
  doi     = {10.5281/zenodo.21812717},
  url     = {https://github.com/Ziaeemehr/JaxCont}
}

JaxCont is distributed under the MIT License.