Autoresonance in Klein-Gordon Chains
In this paper we study the emergence and stability of autoresonance (AR) in the nonlinear Klein-Gordon chain consisting of identical linearly coupled Duffing oscillators. The chain is excited by an external periodic force with a slowly varying frequency applied to one of the oscillators. Explicit asymptotic equations describing the averaged amplitudes and phases of oscillations are derived. These equations demonstrate that, in contrast to the chains with linear attachments, the nonlinear chain can be entirely captured into resonance.
As shown in this paper, AR in the entire chain gives birth to the asymptotic equipartition of energy amongst the oscillators, which is manifested as the convergence of the amplitudes of oscillations to a monotonically increasing mean value equal for all oscillators. The
thresholds of the structural and excitation parameters, which allow the emergence of AR in the entire chain, are determined. The derived analytic results are in good agreement with numerical simulation.
CYBERNETICS AND PHYSICS, Vol. 5, No. 4, 2016 , 123–129.