Eur. Phys. J. B (2014) 87: 65
https://doi.org/10.1140/epjb/e2014-41070-1

Regular Article

Liénard-type chemical oscillator

Indian Association for the Cultivation of Science, Jadavpur, 700032 Kolkata, India

^a e-mail: pcdsr@iacs.res.in

Received: 11 December 2013
Published online: 12 March 2014

Abstract

We show that a class of arbitrary, autonomous kinetic equations in two variables describing chemical and biochemical oscillations can be reduced to the form of a Liénard oscillator. The basis of this reduction scheme is a set of linear transformations of the original variables into a new set of variables which can be found by direct inspection of the kinetic equations. Our study reveals that despite their diverse origin, these kinetic equations when cast as a Liénard system form a universality class, make it possible to identify the forcing term as well as the nonlinear damping coefficient responsible for dynamical control of the underlying limit cycle behavior.