A simple soft limiter describing function for biomedical applications

This paper suggests an arctangent function as a suitable parameterisation for the soft-limiting gain characteristic frequently encountered in models of biomedical systems. This function is shown, as an example, to fit the neural arc component of the baroreflex with the main contribution of the paper being the development of a simple describing function (DF) characteristic for the arctangent. The simple form of the DF allows transparency of the physiological parameters in, for example, stability analysis. For illustration, the derived DF is used to examine low-frequency limit cycles in blood pressure, sometimes termed Mayer waves.