Unusual Liénard-type nonlinear oscillator

V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan
Phys. Rev. E 72, 066203 – Published 2 December 2005

Abstract

A Liénard type nonlinear oscillator of the form ẍ+kxẋ+(k29)x3+λ1x=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 λ1>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 λ10 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.

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  • Received 13 August 2004

DOI:https://doi.org/10.1103/PhysRevE.72.066203

©2005 American Physical Society

Authors & Affiliations

V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan

  • Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirappalli-620 024, India

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Issue

Vol. 72, Iss. 6 — December 2005

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