1. Minimum models of damped and limit cycle oscillations in a polymerization
- Author
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Katime, Issa, Pérez Ortiz, Juan A., Zuluaga, Fabio, and Mendizábal, Eduardo
- Subjects
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MATHEMATICAL models , *DAMPING (Mechanics) , *LIMIT cycles , *OSCILLATIONS , *POLYMERIZATION , *SCHEMES (Algebraic geometry) , *MONOMERS , *ADDITION reactions - Abstract
Abstract: A simple polymerization scheme has been studied introducing small modifications leading to a stable focus type steady state (with damped oscillations) or unstable focus type (which combined with a no return enclosure for phase trajectories will show cycle limit sustained oscillations). Two variables have been employed in this analysis: X∝ monomer, . Limit cycle oscillations requires the addition of autocatalysis with respect to the monomer, J+X→2X, and so does an “enzymatic” block assuming that . The combination of both collateral additions makes the steady state an unstable focus and allows a simple Poincaré–Bendixson proof for the existence of the limit cycle. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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