Module continuation 

Numerical continuation and bifurcation analysis.

Implements pseudo-arclength continuation for tracking solution branches of parameterised nonlinear systems F(u, λ) = 0, together with fold and bifurcation point detection, branch switching, turning-point location, stability analysis, and generic path-following with event detection.

Structs

BifurcationPoint

A bifurcation point detected along a branch.

BranchSwitching

Bordered-system branch switching at a bifurcation point.

ContinuationState

State along a continuation branch.

CorrectorResult

Result of a Newton corrector iteration.

PathFollowing

Generic path-following algorithm with event detection.

PathStep

Result of a single path-following step.

PseudoArcLengthContinuation

Configuration and state for pseudo-arclength continuation.

StabilityAnalysis

Stability analysis along a continuation branch.

TurningPointLocator

Locator for turning (fold) points using bisection on the determinant.

Enums

BifurcationType

Classification of a detected bifurcation.

StabilityLabel

Assignment of stability to a solution branch point.

Functions

branch_switching

Switch to a secondary branch at a detected bifurcation point.

classify_bifurcation

Classify the bifurcation between two consecutive continuation states.

corrector_newton

Newton corrector for pseudo-arclength continuation.

detect_bifurcation

Detect a bifurcation point by checking whether any eigenvalue of the Jacobian changes sign between two consecutive states.

detect_fold_point

Detect a fold (limit) point by checking for a sign change in the determinant of the Jacobian along two consecutive states.

matrix_determinant

Compute the determinant of a square matrix (row-major Vec<Vecf64>).

pseudo_arclength_step

Advance the continuation state by one predictor step.

stability_index

Count the number of eigenvalues with positive real part (unstable eigenvalues) of a square real matrix.