Journal of Dynamics and Differential Equations

, Volume 22, Issue 3, pp 491–507

Nonlinear Oscillations and Multiscale Dynamics in a Closed Chemical Reaction System



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.


Closed chemical reaction Reversible Lotka–Volterra system Multi-scale dynamics Nonlinear oscillation Singular perturbation 

Mathematics Subject Classification (2000)

34C15 34E15 37L45 92E20 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  3. 3.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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