Instability and Chaos in Non-Linear Wave Interaction: a simple model

I. M. Khalatnikov; M. Kroyter

doi:10.1134/1.558838

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arXiv · chao-dyn/9809017

Instability and Chaos in Non-Linear Wave Interaction: a simple model

I. M. Khalatnikov·M. Kroyter

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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.

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I. M. Khalatnikov, M. Kroyter. 1998-09-23. Instability and Chaos in Non-Linear Wave Interaction: a simple model. https://doi.org/10.1134/1.558838

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