  We investigate energy transfer and localization in a linear time-invariant
oscillator chain weakly coupled to a forced nonlinear actuator. Two types of
perturbation are studied: (1) harmonic forcing with a constant frequency is
applied to the actuator (the Duffing oscillator) with slowly changing
parameters; (2) harmonic forcing with a slowly increasing frequency is applied
to the nonlinear actuator with constant parameters. In both cases, stiffness of
linear oscillators as well as linear coupling remains constant, and the system
is initially engaged in resonance. The parameters of the systems and forcing
are chosen to guarantee autoresonance (AR) with gradually increasing energy in
the nonlinear actuator. As this paper demonstrates, forcing with constant
frequency generates oscillations with growing energy in the linear chain but in
the system excited by forcing with slowly time-dependent frequency energy
remains localized on the nonlinear actuator whilst the response of the linear
chain is bounded. This means that the systems that seem to be almost identical
exhibit different dynamical behavior caused by their different resonance
properties. Numerical examples a good agreement between exact (numerical)
solutions and their asymptotic approximations found by the multiple time scales
method.
