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• W2045161071 abstract "A Li'enard type nonlinear oscillator of the form $stackrel{ifmmode ddot{}else &#34;{}fi{}}{x}+kxstackrel{ifmmode dot{}else .{}fi{}}{x}+({k}^{2}∕9){x}^{3}+{ensuremath{lambda}}_{1}x=0$, which may also be considered as a generalized Emden-type equation, is shown to possess unusual nonlinear dynamical properties. It is shown to admit explicit nonisolated periodic orbits of conservative Hamiltonian type for ${ensuremath{lambda}}_{1}>0$. These periodic orbits exhibit the unexpected property that the frequency of oscillations is completely independent of amplitude and continues to remain as that of the linear harmonic oscillator. This is completely contrary to the standard characteristic property of nonlinear oscillators. Interestingly, the system though appears deceptively a dissipative type for ${ensuremath{lambda}}_{1}ensuremath{leqslant}0$ does admit a conserved Hamiltonian description, where the characteristic decay time is also independent of the amplitude. The results also show that the criterion for conservative Hamiltonian system in terms of divergence of flow function needs to be generalized." @default.
• W2045161071 created "2016-06-24" @default.
• W2045161071 creator A5029366908 @default.
• W2045161071 creator A5034624285 @default.
• W2045161071 creator A5046071226 @default.
• W2045161071 date "2005-12-02" @default.
• W2045161071 modified "2023-09-23" @default.
• W2045161071 title "Unusual Liénard-type nonlinear oscillator" @default.
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• W2045161071 doi "https://doi.org/10.1103/physreve.72.066203" @default.
• W2045161071 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/16486036" @default.
• W2045161071 hasPublicationYear "2005" @default.
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