Exact Discrete-Time Implementation of the Mackey–Glass Delayed Model

Abstract

The celebrated Mackey-Glass (MG) model describes the dynamics of physiological delayed systems, in which the actual evolution depends on the values of the variables at some previous times. This kind of system is usually expressed by delayed differential equations, which turn out to be infinite dimensional. In this brief, an electronic implementation mimicking the MG model is proposed. New approaches for both the nonlinear function and the delay block are made. Explicit equations for the actual evolution of the implementation are derived. Simulations of the original equation, the circuit equation, and experimental data show great concordance.