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Liénard-type chemical oscillator

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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.

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Authors and Affiliations

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

    Shyamolina Ghosh & Deb Shankar Ray

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  1. Shyamolina Ghosh
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  2. Deb Shankar Ray
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Correspondence to Deb Shankar Ray.

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Ghosh, S., Ray, D. Liénard-type chemical oscillator. Eur. Phys. J. B 87, 65 (2014). https://doi.org/10.1140/epjb/e2014-41070-1

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