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Statement of need/field
Lyapunov exponents
How lyapax is implemented
Validation: how lyapax’s results are checked
Capabilities and limitations
JAX performance notes
Benchmarks
Examples
Sanity check: watch the time series before trusting the exponents
Linear ODE: exact Lyapunov spectrum
Writing your own system: no registry needed
Chaotic maps: exact analytic Lyapunov exponents
Chaotic flows: Lorenz and Rossler
Coupled linear network: exact eigenvalues
Kuramoto network: synchronization transition
Custom coupling functions: no registry needed
Speed and accuracy characterization
Delayed coupling: two-node linear DDE network vs delay
Kuramoto network with delayed coupling: what transmission delay does
Matrix-free tangent propagation: dense jacfwd vs jvp/vmap
vmap parameter sweeps: the same Kuramoto transition, one XLA call
The lyapax front door: problem objects for ODEs, networks, and DDEs
DDE history reads: grid-snapped vs Hermite-interpolated
GPU acceleration: when does it actually pay off?
Adaptive-step ODE integration (diffrax)
Convergence diagnostics: convergence_drift + resume
Resuming a DDE run: convergence_drift + resume, ring-buffer edition
Differentiating a Lyapunov exponent w.r.t. a system parameter
Kaplan-Yorke (Lyapunov) dimension
API reference
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