A numerical and analytical study of floquet multipliers of periodic solutions near a homoclinic orbit

We derive an analytical estimate for the Floquet multipliers of periodic so lutions of a 2D system near a homoclinic orbit at a fixed point of saddle t ype. We will demonstrate numerically what happens for higher-dimensional sy stems. We will also numerically investigate two cases of a homoclinic orbit in three-dimensional systems with one positive real eigenvalue and a pair of complex conjugate eigenvalues with negative real part at the saddle poin t.