Limit cycles that do not comprise steady states of reactors

It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested numerically. The above-mentioned phenomenon is characterized by the location of the steady point out of the limit cycle in the phase portrait. This incident may be beneficial to the process, as low steady state does not have to exclude an independent increase of the conversion degree, despite being the only state and not generating oscillations.Comment: 9 pages, 6 figures, the paper is printed in Applied Mathematics and Computation, vol. 312, pp. 129-133, 201

Existence and Uniqueness of Limit Cycles in an Enzyme-Catalysed Reaction System

An enzyme-catalysed reaction system arising from glycolysis is investigated. By using the qualitative theory of ordinary dierential equations, sucient conditions are obtained for the existence, nonexistence and uniqueness of limit cycles of the systems. Numerical continuation methods reveal the occurrence of large period solutions resulting from an almost homoclinic connection on a saddle point. Keywords{Enzyme-catalysed, Limit cycle, Global stability. 1 Introduction In this paper we consider a class of systems of the type proposed in [1] and discussed in [2], used there to model a biochemical reaction in which a substrate, s, is converted to a product, p, and a sink. Many such reactions are present in actual biochemical systems with the specic example dealt with in [1] being related to glycolysis in yeast cells (see [3] and also [5] for a review of similar models and how they are used to investigate the qualitative properties of biochemical reactions). The model takes the followin..