Crate oldies_auto 

AUTO-RS: AUTO Continuation/Bifurcation Software Revival

Revival of AUTO continuation/bifurcation software in Rust. Originally created by Eusebius Doedel (1980s) at Concordia University.

AUTO is the gold standard for numerical continuation and bifurcation analysis of ODEs, PDEs, and algebraic equations.

This crate provides:

• Natural parameter continuation
• Pseudo-arclength continuation
• Bifurcation detection (saddle-node, Hopf, branch points)
• Stability analysis via eigenvalue computation
• Branch switching at bifurcation points

Reference: Doedel, E.J. et al. AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations.

Structs

BifurcationPoint

Bifurcation point information

Brusselator

Brusselator: famous chemical oscillator

ComputationStats

Computation statistics

ContinuationBranch

Result of a continuation run

ContinuationParams

Continuation control parameters (like AUTO’s constants file)

FoldNormalForm

Fold (saddle-node) normal form: dx/dt = mu - x^2

HopfNormalForm

Hopf normal form: dx/dt = mux - y - x(x^2+y^2), dy/dt = x + muy - y(x^2+y^2)

LorenzSystem

Lorenz system

PitchforkNormalForm

Pitchfork normal form: dx/dt = mu*x - x^3

SolutionPoint

A point on the continuation branch

Enums

AutoError

BifurcationType

Types of bifurcations detected

Traits

OdeSystem

Trait for ODE systems to be continued

Functions

arclength_continuation

Pseudo-arclength continuation Parameterizes the curve by arclength to handle turning points

branch_switch

Switch to a new branch at a bifurcation point

compute_eigenvalues

Compute eigenvalues of a matrix using QR iteration

natural_continuation

Natural parameter continuation Simple method that just varies the parameter and solves at each step

newton_solve

Newton’s method for finding roots of F(x) = 0

Type Aliases

Result