A relay Mackey–Glass model with two delays

We study the dynamics of the generalized Mackey–Glass equation with two delays using the large-parameter method. After a special exponential replacement of variables, a singularly perturbed equation is obtained, for which we construct a meaningful limit object, a differential–difference relay equation with two delays. We prove that the relay equation has a simple periodic solution with one interval on the period where the solution is positive. To illustrate the obtained result, we numerically analyze the original singularly perturbed equation, for which we find a solution near the periodic solution of the limit relay equation.