Journal
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume 22, Issue 3, Pages 491-507Publisher
SPRINGER
DOI: 10.1007/s10884-010-9156-3
Keywords
Closed chemical reaction; Reversible Lotka-Volterra system; Multi-scale dynamics; Nonlinear oscillation; Singular perturbation
Categories
Funding
- Institute for Mathematics and its Applications
- NSF [DMS0708331]
- NSFC [10428101]
- Jilin University
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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.
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