jaxcont 0.3.0

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.

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, and direct codimension-two point solvers. Branch switching, general connecting-orbit/BVP workflows, PRC/dPRC, and two-parameter curve continuation remain future work.

Installation

JaxCont requires Python 3.9 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

• 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, cite the archived release using its GitHub/Zenodo DOI. Citation metadata is provided in CITATION.cff. Until the first archive is minted:

@software{ziaeemehr_jaxcont_2026,
  author  = {Ziaeemehr, Abolfazl},
  title   = {JaxCont: Differentiable Continuation and Bifurcation Analysis in JAX},
  year    = {2026},
  version = {0.3.0},
  url     = {https://github.com/Ziaeemehr/JaxCont}
}

JaxCont is distributed under the MIT License.