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getLinearlyStableSolutions -- Compute linearly stable solutions for the Kuramoto oscillator system associated to a graph

Description

The function getLinearlyStableSolutions computes the linearly stable solutions for the Kuramoto oscillator system associated to a given graph. The Kuramoto oscillator system is a system of coupled phase oscillators, where the dynamics of each oscillator is given by the Kuramoto model. The linear stability of a solution is determined by the eigenvalues of the Jacobian matrix of the system evaluated at the solution.

i1 : G = graph({0,1,2,3}, {{0,1},{1,2},{2,3},{0,3}});
i2 : getLinearlyStableSolutions(G)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)
 -- .121512s elapsed
warning: some solutions are not regular: {4, 5, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}

o2 = {{1, 1, 1, 0, 0, 0}}

o2 : List

See also

Ways to use getLinearlyStableSolutions:

  • getLinearlyStableSolutions(Graph)

For the programmer

The object getLinearlyStableSolutions is a method function.


The source of this document is in Oscillators/Documentation.m2:567:0.