, Volume 22, Issue 3, pp 491-507
Date: 02 Feb 2010

Nonlinear Oscillations and Multiscale Dynamics in a Closed Chemical Reaction System

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Abstract

We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka–Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka–Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regions in the phase space, that is, while orbits ultimately reach the equilibrium in a non-oscillatory fashion, they exhibit damped, oscillatory behaviors as interesting transient dynamics.

Dedicated to Professor Jack K. Hale on the occasion of his 80th birthday.