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Oscillators : Table of Contents
Oscillators
-- generation and analysis of oscillator steady states for small graphs
allUniquePrincipalMinors
-- Compute all unique principal minors of a given matrix
Checking the codimension and irreducible decomposition of the IG ideal
-- generating all SCT graphs on n vertices
Example 4.1: unique graph on 8 vertices with exotic solutions and no induced cycle of length at least 5
-- example 4.1 in arXiv 2312.16069
Example 4.2: a K5 and pentagon glued along an edge
-- example 4.2 in arXiv 2312.16069
Example 4.3: examples of gluing two cycles along an edge
-- example 4.3 in arXiv 2312.16069
Example 4.4: The square within a square
-- example 4.4 in arXiv 2312.16069
findRealSolutions
-- find real solutions, at least one per component for well-conditioned systems
Generation of all SCT (simple, connected, 2-connected) graphs on small numbers of vertices
-- generating all SCT graphs on n vertices
getAngles
-- Compute angles from a list of solutions
getLinearlyStableSolutions
-- Compute linearly stable solutions for the Kuramoto oscillator system associated to a graph
Harrington-Schenck-Stillman
-- Arxiv 2312.16069 reference
identifyStability
-- Identify the stability of a list of eigenvalues, or of potential solutions to the oscillator system
isStableSolution
-- Check if a given solution is stable for the Kuramoto oscillator system
oscJacobian
-- create the Jacobian for the oscillator system associated to a graph
oscQuadrics
-- find the homogeneous quadrics in the homogeneous Kuramoto ideal
oscRing
-- create a polynomial ring for a given graph or number of oscillators
oscSystem
-- the ideal of the reduced equilibrium points of a dynamical system of oscillators
SCT graphs with exotic solutions
-- finding graphs of small size with exotic solutions
showExoticSolutions
-- Display exotic solutions: linearly stable solutions which are not all-in-phase solution
standardSols
-- find the "standard solutions" for the oscillator system associated to a graph
vertexSpanningPolynomial
-- computes the vertex spanning polynomial