Damage-induced paths in the partially homogenized dynamics of complex networks

We consider complex lattices whose elementary constituents are interacting sub-lattices. A Cauchy–Born-type matching rule at the sublattice level leads to a partially homogenized Hamiltonian description in which translational and coarse microstructural degrees of freedom coexist. Under T -periodic external forcing, we establish the existence of T -periodic motions under a suitable non-T -resonance condition. Structural damage modifies the Hamiltonian itself and induces a corresponding spectral evolution. For an FPUT-type chain with an additional internal degree of freedom, chosen as a prototype example, we show that monotone bond degradation can produce a transversal resonance crossing and a local bifurcation of periodic motions. The same transition is characterized through the Poincaré map and, under nonzero forcing, unfolds into a local fold of T -periodic solutions.