Semi-Resonant Interactions and Frequency Dividers

M. J. Ablowitz, B. A. Funk, A. C. Newell

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A theory describing the behavior of a system as it evolves slowly through internal nonlinear resonances is presented. The energy sharing process is seen to be quite complex as it depends crucially on both nonlinear and frequency detuning effects. Two phenomena are discussed in detail although the general ideas are applicable to many situations. Firstly we examine the interaction between the quadratically coupled oscillators whose natural frequencies are in the ratio 2:1 for a limited period of time. Such a system is shown to be an extremely useful switching device. Secondly we examine the time dependent Duffing equation and find that smooth forward and reverse transitions occur without the presence of dissipation.

Original languageEnglish (US)
Pages (from-to)51-74
Number of pages24
JournalStudies in Applied Mathematics
Issue number1
StatePublished - Mar 1 1973

ASJC Scopus subject areas

  • Applied Mathematics


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