Floquet multipliers can exit the unit circle in three ways: at (1,0), at exp{\pm i \varphi} or at (-1,0). What is the significance of Floquet multipliers crossing the unit circle at (-1,0) in contrast to (1,0)?
In the context of Floquet theory for time periodic systems, if any eigenvalues of the Monodromy matrix have a real part with modulus >1, the the time periodic solution is unstable. If a real eigenvalue crosses the unit circle at +1, this represents a cyclic-fold or symmetry-breaking bifurcation. If a real eigenvalue crosses the unit circle at -1, this represents a period doubling bifurcation, and if a complex conjugate pair crosses the unit circle, this represents a secondary Hopf or Niewmark bifurcation. I have attached a PDF that shows how these calculations can be done using Mathematica to study the stability of periodic equations using Floquet theory
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