STABILITY OF CONTROLLED BIOLOGICAL SYSTEMS

The stability properties of a biochemical feedback system of the Yates-Pardee type are studied. The stability of the linear system is ascertained by identifying the nature of the roots of the characteristic equation of the linear differential equations. A necessary condition for sustained concentration oscillations resulting from small perturbations of the steady state is derived from a closure rule. The stability properties and conditions for which sustained oscillations are possible for a non-linear feedback system of this type are mapped; the results applicable to the non-linear system were obtained using a variation of the direct Lyapunov method. The use of this method is illustrated with an example application. © 1969.