Application of digital control theory to exact discretization of a logistic equation with a constant term

This paper presents an exact method of discretizing a logistic differential equation with a constant term (a class of Riccati equation), which are prevalent in a variety of fields, using a common knowledge in digital control theory. The resulting model gives the value that is exact at the discrete-time instants for any discretization period. Two existing methods that can lead to an exact discrete-time model are second-order and shown to be based on diverging variables, while the one proposed in this study is first-order and not prone to such a numerical problem. A simulation result is presented to illustrate this issue