Autoresonant interaction of three nonlinear adiabatic oscillators

The autoresonance phenomenon in a system of three weakly interacting nonlinear oscillators with slowly varying parameters is studied. When excited, the triple autoresonant interaction yields an efficient and continuous energy exchange between the oscillators while the nonlinear resonance condition is preserved, despite the variation of the parameters of the system. It is shown that the autoresonance is stable with respect to the addition of sufficiently small friction and fluctuations in the system. The amount of the allowed noise is estimated and the theory is illustrated by numerical examples.