Limit Cycles in Reaction Systems with Second Order Autocatalysis
As a model for biochemical reactions the autocatalytic formation of the reactand X from a raw material Y is studied. It is shown that the system forms limit cycles; numerical examples are presented. As a second problem the above reaction is considered in the case of two boxes coupled by linear diffusion exchange of the raw material which is described by a term D(Y1 - Y2) (Yi - concentration in box i). In the case of weak coupling in both boxes beating between two frequencies are found. In the case of strong coupling damped oscillations and disappearance of Xi in one box are observed. The third problem is the stochastic theory of the given reactions. the corresponding master-equation is formulated and properties of the solution are discussed. Results of a computer simulation of the given birth and death process are represented.