Isochronicity and limit cycle oscillation in chemical systems

TL;DR

This paper investigates the conditions for limit cycle oscillations and isochronicity in chemical systems using Lienard equations and renormalization group methods, providing a unified framework for understanding nonlinear chemical oscillators.

Contribution

It introduces a unified approach to determine limit cycle and isochronicity conditions in chemical oscillators via Lienard systems and renormalization group analysis.

Findings

Derived conditions for limit cycle oscillation.

Established criteria for isochronicity in chemical oscillators.

Showed transformation routes from limit cycles to center-type orbits.

Abstract

Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a limit cycle around an interior stationary point. In this context Lienard equation is specifically used in the study of nonlinear dynamical properties of an open system which can be utilized to obtain the condition of limit cycle. In conjunction with the property of limit cycle oscillation, here we have shown the condition for isochronicity for different chemical oscillators with the help of renormalisation group method with multiple time scale analysis from a Lienard system. When two variable open system of equations are transformed into a Lienard system of equation the condition for limit cycle and isochronicity can be stated in a unified way. For any such nonlinear oscillator we have shown the route of a dynamical transformation of a limit cycle oscillation to a periodic orbit of centre type depending on the parameters of the system.