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Instability and chaos in nonlinear wave interaction: A simple model

  • I. M. Khalatnikov
  • M. Kroyter
Nonlinear Physics

Abstract

We analyze the stability of a system which contains a harmonic oscillator nonlinearly 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 of greater amplitude, chaotic behavior is observed. The generalization to interactions which include higher modes is discussed.

Keywords

Spectroscopy State Physics Field Theory Elementary Particle Simple Model 
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Copyright information

© American Institute of Physics 1999

Authors and Affiliations

  • I. M. Khalatnikov
    • 1
    • 2
  • M. Kroyter
    • 3
  1. 1.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.L. D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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