Instability of the Breathers

Instabilities and resonances correspond to collisions of an eigenvalue of Floquet matrix with complex conjugated partner on the positive real axis (primary resonance), on the negative real axis (parametric resonance) or to the collision of two different eigenvalues away from the real axis (combination resonance).
 
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[3] A. Benabdallah, M. V. Fistul and S. Flach, Breathers in a single plaquette of Josephson junctions: existence, stability and resonances, Physica D 159(2001) 202-214.