Reduction of Kinetic Equations to Liénard–Levinson–Smith Form: Counting Limit Cycles View Full Text


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Article Info

DATE

2019-03-29

AUTHORS

Sandip Saha, Gautam Gangopadhyay, Deb Shankar Ray

ABSTRACT

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard–Levinson–Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov–Boguliubov (K–B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases. More... »

PAGES

46

References to SciGraph publications

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  • 2010-11-10. Counting limit cycles with the help of the renormalization group in THE EUROPEAN PHYSICAL JOURNAL D
  • 2017-01-06. Isochronicity and limit cycle oscillation in chemical systems in JOURNAL OF MATHEMATICAL CHEMISTRY
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  • 2015-03-24. Finding Limit Cycles in self-excited oscillators with infinite-series damping functions in THE EUROPEAN PHYSICAL JOURNAL D
  • 2018-11-09. When an oscillating center in an open system undergoes power law decay in JOURNAL OF MATHEMATICAL CHEMISTRY
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    http://scigraph.springernature.com/pub.10.1007/s40819-019-0628-9

    DOI

    http://dx.doi.org/10.1007/s40819-019-0628-9

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