Transient traveling breather response of strongly anharmonic array of self-sustained oscillators: Analytical study

In the present study, we analyze the transient response of a locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely nonlinear, aeroelastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, finite chains of self-sustained oscillators. The genuinely anharmonic nature of the system under consideration turns the asymptotic analysis of the transient regimes arising in this type of model into 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 the amplitude evolution of the breather core towards the steady state as well as its instantaneous position.