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Existence of periodic solutions for enzyme-catalysed reactions with periodic substrate input

Pages: 551 - 557, Issue Special, September 2007

 Abstract        Full Text (175.6K)              

Guy Katriel - Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel (email)

Abstract: Considering a basic enzyme-catalysed reaction, in which the rate of input of the substrate varies periodically in time, we give a necessary and sufficient condition for the existence of a periodic solution of the reaction equations. The proof employs the Leray-Schauder degree, applied to an appropriately constructed homotopy.

Keywords:  Enzyme kinetics, periodic forcing, periodic solutions, topological degree.
Mathematics Subject Classification:  Primary: 92C45, 34C25; Secondary: 47H11.

Received: August 2006;      Revised: April 2007;      Published: September 2007.