The monodromy matrix is defined for a periodic system \(u(t)\) with period \(T\) and initial value \(z\).
$$M=\frac{\delta\phi(T;z)}{\delta z}$$
Where \(\phi(T;z)\) is a trajectory that solves \(u(0)=\phi\). One of the eigenvalues, also called Floquet Multipliers, of the monodromy matrix is always 1. The moduli of the remaining eigenvalues determines the stability of the system. If the moduli of all of the remaining eigenvalues are less than 1, then the system is stable. If any eigenvalue has a modulus of greater than one, then the system is unstable.
[[Floquet Multiplier]]
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