Exact solutions for discrete breathers in a forced-damped chain

Oleg Gendelman (1)

1 Department of Mechanical Engineering [Haifa]

Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

Domaines: Sciences de l'ingénieur [physics]

Oleg Gendelman. Exact solutions for discrete breathers in a forced-damped chain. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 87, pp.062911. ⟨10.1103/PhysRevE.87.062911⟩. ⟨hal-01510820⟩