Summary
In the present study, we analyze the transient response of locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely non-linear, aero-elastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, homogeneous and inhomogeneous chains of self-sustained oscillators. The genuinely anharmonic nature of system under consideration, turns the asymptotic analysis of transient regimes arising in this type of models to a highly challenging task. In the present study, we formulate a special analytical approach which allows for a simple, explicit and fairly accurate analytical description of amplitude evolution of the breather core towards the steady-state as well as its instantaneous position.
