ABSOLUTE STABILITY OF CERTAIN TYPES OF CONTROLLED BIOLOGICAL SYSTEMS

The differential equations describing chemical control systems of the Yates-Pardee (1956) type are put into a canonical form with the aid of the Lur'e (1951) transformation. The stability properties of the transformed equations are examined by methods based on the second Lyapunov theorem. The results illustrate that sustained concentration oscillations cannot arise in controlled biochemical reactions of the type described by equations (1), n = 1. For n > 1, the nature of the non-linear feedback function determines whether or not sustained oscillations can arise in the chemical control systems. It is shown, however, that even if these constants assume certain values in the prescribed range, sustained oscillations do not in fact arise. Digital computer simulations provided no indication that sustained concentration oscillations can arise in chemical control systems described by equations (1), n =1, n = 2 and n = 3. © 1969.