Related Experiment Video
Updated: Aug 7, 2026

Fabrication and Characterization of Superconducting Resonators
Published on: May 21, 2016
Effect of resonant-frequency mismatch on attractors
Xingang Wang1, Ying-Cheng Lai, Choy Heng Lai
1Department of Physics, National University of Singapore, Singapore 117542.
Abstract:
Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value. We call such attractors pseudo-strange. The transition to pesudo-strange attractors as a system parameter changes can be understood analytically by regarding the system as nonstationary and using the Melnikov function. Our results imply that pseudo-strange attractors are common in nonstationary dynamical systems.
Related Concept Videos
Concept of Resonance and its Characteristics
Sound Waves: Resonance
Parallel Resonance
Resonance in an AC Circuit
Series Resonance
Design Example: Underdamped Parallel RLC Circuit
Starting with a fixed...

