Instability and Chaos in Non-Linear Wave Interaction: a simple model
chao-dyn
2009-10-31 v1 Statistical Mechanics
Chaotic Dynamics
Abstract
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above which a loss of stability appears. The dependence of the critical input power on the physical parameters is analyzed. For a driving force with higher amplitude chaotic behavior is observed. Generalization to interactions which include higher modes is discussed. Keywords: Non-Linear Waves, Stability, Chaos.
Cite
@article{arxiv.chao-dyn/9809017,
title = {Instability and Chaos in Non-Linear Wave Interaction: a simple model},
author = {I. M. Khalatnikov and M. Kroyter},
journal= {arXiv preprint arXiv:chao-dyn/9809017},
year = {2009}
}
Comments
16 pages, 4 figures