Liénard-type chemical oscillator

摘要

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.