  In this work, we develop an analytical framework to explain the influence of
dissipation and detuning parameters on the emergence and stability of
autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic
forcing with a slowly-varying frequency. Using the asymptotic procedures, we
construct the evolutionary equations, which describe the behavior of the array
under the condition of 1:1 resonance and then approximately compute the slow
amplitudes and phases as well as the duration of autoresonance. It is shown
that, in contrast to autoresonance in a non-dissipative chain with unbounded
growth of energy, the energy in a weakly damped array being initially at rest
is growing only in a bounded time interval up to an instant of simultaneous
escape from resonance of all autoresonant oscillators. Analytical conditions of
the emergence and stability of autoresonance are confirmed by numerical
simulations.
