Where the Liénard--Levinson--Smith (LLS) theorem cannot be applied for a generalised Liénard system

Abstract

We have examined a class of Liénard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et al., CNSNS 85, 105234 (2020) (last para of sec 4.2.2). Here we have provided a physical approach to address this problem using the concept of energy consumption per cycle. We have elaborated the idea through proper demonstration by considering a generalized model system. Such issues have potential utility in nonlinear vibration control.

arXiv commentFour pages, Two figures, Under review

References in corpus (6)

• Center or Limit Cycle: Renormalization Group as a Probe
• Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators
• Isochronicity and limit cycle oscillation in chemical systems
• Cheillini integrability and quadratically damped oscillators
• Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
• When an oscillating center in an open system undergoes power law decay