Delay induced oscillations in autonomous drug delivery systems

Abstract

Drug therapies are often designed to reproduce the physiological uctuations in normal biological agents, including hormones. These regimens entail the need for a periodic, yet sustained administration, and thus require the generation of oscillatory variations in concentrations. We extend (in part, by the explicit use of time-delayed arguments) a system introduced recently along this design, in which the oscillations are generated by the delayed response of the permeability of a membrane at the boundary of a reaction chamber. We completely analyse the stability of the equilibrium, and present conditions under which Hopf bifurcations are present. We also provide further conditions for multiple mode instabilities to occur, by the occurence of double Hopf bifurcations.