Conservative perturbation theory for nonconservative systems

Abstract

In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz.,~Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system--- a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass even wider range of non-conservative systems.

8 Pages, Published in Physical Review E (2015)

References in corpus (1)

• Comment on "Classical Mechanics of Nonconservative Systems"

Cited by in corpus (12)

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• Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction : General results and a case study with Landau Hamiltonian
• Equivalent linearization finds nonzero frequency corrections beyond first order
• Optimal synchronisation to a limit cycle
• Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials
• Quantization of nonlinear non-Hamiltonian systems
• Geometric numerical integration of Liénard systems via a contact Hamiltonian approach
• Complex dynamical properties of coupled Van der Pol-Duffing oscillators with balanced loss and gain
• Time-optimal synchronisation to self-sustained oscillations under bounded control