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The character of the singular points at infinity is not affected by variations of input flux. The situation is slightly more complicated for the system with enzymatic output. As opposed to the previous system, the singular point SP1 is now located inside the first quadrant only for particular values of rate constants and input flux. The requirement that SP1 must have a positive index imposes further restrictions on the values of these parameters. In this case, but depending on the values of V m and ί^ of the output reaction and the rate constant of the feedback step, the singular point is either stable for all permissible values of input flux or stable for low, unstable for intermediate, and stable for high flux values.
Reaction mechanism and differential equation for Lotka's second mechanism· Figure 8. Global phase portrait for Lotka1s second mechanism. 38 BIOCHEMICAL OSCILLATORS Discussion An excellent basis for a comparative evaluation of the systems just introduced is provided by the input flux, which in each case was assumed to be independent. In Lotka's first mechanism, both position and character of the single stationary state depend on the amount of flux into the system. We find, in particular, that for small input fluxes the singular point which represents this state in the phase portrait is a stable focus with the associated damped oscillations.
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