Nonlinear turnover models for systems with physiological limits

In this paper we propose a new approach with either one (lower or upper) limit or two (simultaneously acting lower and upper) limits (dual limits). We present an analytical mathematical treatment as well as a numerical treatment via model simulations. This approach allows for a baseline value to be only weakly dependent on the lower/upper physiological limit. It also allows dual limits, one below and one above, which is attractive because it may be applicable to commonly studied physiological and biochemical systems such as turnover of water or fat.