Nonlinear Oscillations and Multiscale Dynamics in a Closed Chemical Reaction System

Authors: Li, Yongfeng¹; Qian, Hong²; Yi, Yingfei³

Source: Journal of Dynamics and Differential Equations, Volume 22, Number 3, September 2010 , pp. 491-507(17)

Publisher: Springer

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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.

Keywords: Closed chemical reaction; Reversible Lotka-Volterra system; Multi-scale dynamics; Nonlinear oscillation; Singular perturbation; 34C15; 34E15; 37L45; 92E20

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10884-010-9156-3

Affiliations: 1: Institute for Mathematics and its Applications, University of Minnesota, 207 Church St. S.E., Minneapolis, MN, 55455-0134, USA, Email: yonli@ima.umn.edu 2: Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA, Email: qian@amath.washington.edu 3: School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA, Email: yi@math.gatech.edu

Publication date: 2010-09-01