  An energy-based theory of autoresonance in driven dissipative chains of
coupled generic oscillators is discussed on the basis of a variational
principle concerning the energy functional. The theory is applied to chains of
delayed Duffing-Ueda oscillators and the equations that together govern the
autoresonance forces and solutions are derived and solved analytically for
generic values of parameters and initial conditions, including the case of
quenched time-delay disorder. Remarkably, the presence of retarded potentials
with time-delayed feedback drastically modify the autoresonance scenario
preventing the growth of the energy oscillation over specific regions of the
parameter space. Additionally, effective harmonic forces with a slowly varying
frequency are derived from the exact autoresonant excitations and the
effectiveness of the theory is demonstrated at suppressing the chaos induced by
homogeneous periodic excitations in such oscillator chains. Numerical
experiments confirmed all the theoretical predictions.
