화학공학소재연구정보센터
Chemical Engineering Science, Vol.65, No.23, 6292-6295, 2010
Minimum models of damped and limit cycle oscillations in a polymerization
A simple polymerization scheme {X -> R-1 R-j+X -> Rj+1 (j = 1, 2, ... , infinity) R-i+R-j -> polymer (i = 1, 2, ... , infinity) 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 proportional to monomer, Y alpha Sigma(infinity)(j=1) R-j = radicals. Limit cycle oscillations requires the addition of autocatalysis with respect to the monomer, J+X -> 2X, and so does an "enzymatic" block {U+X -> V V -> U assuming that U = 0. TThe combination of both collateral additions makes the steady state an unstable focus and allows a simple Poincare-Bendixson proof for the existence of the limit cycle. (C) 2010 Elsevier Ltd. All rights reserved.