Some conditions for sustained oscillations in chain processes with feedback inhibition and saturable removal

A biochemical chain with feedback inhibition, enzymatic removal and catalyzed input is considered. Some conditions on the parameters are given for which the result is a simple limit cycle behavior or a limit cycle surrounding an unstable limit cycle and a stable point. In the latter case, the system in the steady state can either be at rest or oscillate around the point at rest, depending on the initial conditions. Presented at the May 23–24, 1975 meeting of the Society for Mathematical Biology, Bowling Green State University, Bowling Green, Ohio.