Unusual Lienard-type nonlinear oscillator

Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2005) Unusual Lienard-type nonlinear oscillator Physical Review E, 72 (6). 066203_1-066203_8. ISSN 1063-651X

PDF - Publisher Version

Official URL: http://link.aps.org/doi/10.1103/PhysRevE.72.066203

Related URL: http://dx.doi.org/10.1103/PhysRevE.72.066203


A Lienard type nonlinear oscillator of the form x..+kxx.+(k2/9)x31x=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 λ1 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.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:19394
Deposited On:22 Nov 2010 12:40
Last Modified:17 May 2016 03:57

Repository Staff Only: item control page