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isStableSolution -- Check if a given solution is stable for the Kuramoto oscillator system

Description

The function isStableSolution checks if a given solution is stable for the Kuramoto oscillator system. The stability of a solution is determined by the eigenvalues of the Jacobian matrix of the system evaluated at the solution. If all eigenvalues have negative real parts, the solution is considered stable.

i1 : G = graph({0,1,2,3}, {{0,1},{1,2},{2,3},{0,3}});
i2 : R = oscRing(G, Reduced => true);
i3 : I = oscSystem(G, R);

o3 : Ideal of R
i4 : Jac = oscJacobian(G, R);

             4      4
o4 : Matrix R  <-- R
i5 : realsols = findRealSolutions I;
warning: some solutions are not regular: {9, 10, 14, 16, 19}
i6 : select(realsols, S -> isStableSolution(Jac, S))

o6 = {{1, 1, 1, 0, 0, 0}}

o6 : List

See also

Ways to use isStableSolution:

  • isStableSolution(Matrix,List)

For the programmer

The object isStableSolution is a method function.


The source of this document is in Oscillators/Documentation.m2:677:0.