Discrete breathers in an array of self-excited oscillators: exact solutions and stability

摘要

Dynamics of array of coupled self-excited oscillators is considered. Model ofFranklin bell is adopted as a mechanism for the self-excitation. The modelallows derivation of exact analytic solutions for discrete breathers (DBs), andextensive exploration of their stability in the space of parameters. The DBsolutions exist for all frequencies in the attenuation zone, but lose stabilityvia Neimark-Sacker bifurcation near the boundary of propagation zone. Besidesthe well-known DBs with exponential localization, the considered systempossesses additional and novel type of solutions - discrete breathers with mainfrequency in the propagation zone of the chain. The amplitude of oscillationsin this solution is maximal at the localization site and then exponentiallyapproaches constant value at infinity. We also derive these solutions in closedanalytic form. They are stable in a narrow region of system parameters boundedby Neimark-Sacker and pitchfork bifurcations.