Negative phase velocity in nonlinear oscillatory systems --mechanism and parameter distributions

TL;DR

This paper investigates the mechanism behind negative phase velocity in oscillatory systems using the complex Ginzburg-Landau equation, revealing that wave frequency competition causes antiwaves and establishing criteria applicable across models.

Contribution

It provides a clear physical explanation and general criteria for negative phase velocity in oscillatory media, extending understanding across different models and dimensions.

Findings

Negative phase velocity arises from frequency competition between pacing-induced waves and natural oscillations.

The criteria for negative phase velocity are $ ext{sign}( ext{out}) = ext{sign}( ext{natural})$ and $| ext{out}| < | ext{natural}|$.

No antiwaves or negative phase velocity waves occur in excitable media.

Abstract

Waves propagating inwardly to the wave source are called antiwaves which have negative phase velocity. In this paper the phenomenon of negative phase velocity in oscillatory systems is studied on the basis of periodically paced complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture on the negative phase velocity of these pacing induced waves. This picture tells us that the competition between the frequency $\omega_{out}$ of the pacing induced waves with the natural frequency $\omega_{0}$ of the oscillatory medium is the key point responsible for the emergence of negative phase velocity and the corresponding antiwaves. $\omega_{out}\omega_{0}>0$ and $|\omega_{out}|<|\omega_{0}|$ are the criterions for the waves with negative phase velocity. This criterion is general for one and high dimensional CGLE and for general oscillatory models. Our understanding of antiwaves predicts that no antispirals and waves with negative phase velocity can be observed in excitable media.