Goal-oriented scheme for taming chaos with a weak periodic perturbation: Experiment in a diode resonator

Abstract

We employed the concept of Shannon entropy to characterize the periodicity of the output wave form of a modulated nonlinear diode resonator. A goal-oriented scheme for taming chaos with a weak periodic perturbation is experimentally demonstrated. It is found that a resonancelike regularity is exhibited when the perturbation frequency ${\mathit{f}}_{\mathit{w}}$ follows ${\mathit{f}}_{\mathit{w}}$=${\mathit{f}}_{\mathit{m}}$/n, where ${\mathit{f}}_{\mathit{m}}$ is the modulation frequency and n is an integer. When ${\mathit{f}}_{\mathit{w}}$ is roughly equal to ${\mathit{f}}_{\mathit{m}}$/n and n is small, there exists a low-period orbit, while a larger n results in a high-period orbit. The perturbation's intensity can change the periodicity dramatically; however, as ${\mathit{f}}_{\mathit{w}}$ is chosen to be ${\mathit{f}}_{\mathit{m}}$/n*, the smallest periodicity of the output wave form is n*. This regularity disappears as n becomes too large (\ensuremath{\sim}1000) and other dynamics takes place. \textcopyright{} 1996 The American Physical Society.