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Title: Minimum models of damped and limit cycle oscillations in a polymerization
Author: Katime, I.
Perez Ortiz, J.A.
Zuluaga, F.
Mendizábal, E. M.
Issue Date: 2010
Abstract: A simple polymerization scheme. {X?R1 Rj+X?Rj+1 (j=1,2,...,?) Ri+Rj?polymer (i=1,2,...?j=1,2,...,?) 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, Y??j=1 ?Rj = radicals. Limit cycle oscillations requires the addition of autocatalysis with respect to the monomer, J+. X?2. X, and so does an "enzymatic" block. {U+X?VV?Uassuming that Ü=0. 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. © 2010 Elsevier Ltd.
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