SCALING BEHAVIOR OF THE MAXIMUM ENERGY EXCHANGE BETWEEN COUPLED ANHARMONIC-OSCILLATORS

The maximum energy exchange of two harmonically coupled nonlinear oscillators is investigated. We calculate the maximum energy exchange close to resonance and show that the corresponding resonance curves have a universal shape and become broader and smaller when the amplitude-frequency coupling becomes large. Since there is a large variety of nonlinear oscillators where the trajectories are nearly homothetic curves in a phase-space representation, we furthermore investigate the special situation where the oscillators are homothetic. We argue that in this case there is a scaling of the maximum energy exchange at resonance. Numerical investigations show that these relations remain valid if the oscillators are slightly damped or perturbed by random noise. © 1990 The American Physical Society.