Robustness of nonlinear targeted energy transfer in coupled oscillators to changes of initial conditions

The problem of choosing the appropriate initial conditions for achieving efficient targeted energy transfer (energy pumping) in a system of coupled oscillators with essential nonlinearity is investigated analytically and numerically. The treatment is based on the simplified description of the dynamic flow at the initial stage of motion and up to time scale of O(1). This approach appears to be complimentary to the invariant manifold approach developed in earlier works; hence, the combination of the two approaches allows the complete description of the targeted energy transfer process at its entire time span, and answers the question of robustness of energy transfer to changes of initial conditions.