MATLAB codes for Davide Di Lenarda's MSc thesis in Mathematics, see https://cdlab.uniud.it/theses .

MGequation: Vector field of the Mackey-Glass equation corresponding to the parameters α, β, γ.

MGsolver: Returns the solution of the Mackey-Glass equation and plots the corresponding trajectory.

MGsolvernotran: As MGsolver, but transient behavior is neglected. The input number p in [0, 1] is the last percentage of the solution considered.

MGattractor2D: Plots a two-dimensional projection of the strange attractor. Given an input delay w the function plots the solution x(t) of the Mackey-Glass equation as a function of x(t-w).

MGattractor2Dnotran: As MGattractor2D, but transient behavior is neglected. The input number p in [0, 1] is the last percentage of the solution considered.

MGattractor3D: Plots a three-dimensional projection of the strange attractor. Given two input delays w1, w2 the function plots the solution x(t) of the Mackey-Glass equation as a function of (x(t-w1), x(t-w2)).

MGattractor3Dnotran: As MGattractor3D, but transient behavior is neglected. The input number p in [0, 1] is the last percentage of the solution considered.

MGcrit: The critical points M_n considered are the minima of the x(t-w) coordinate in the two-dimensional projection of the strange attractor given by MGattractor2D. This function plots the critical point M_n as a function of M_{n-1}.

MGtentmin: The critical points M_n considered are the minima of the x(t-w) coordinate lower than the input bound l, in the two-dimensional projection of the strange attractor given by MGattractor2D. This function plots the critical point M_n as a function of M_{n-1}.

MGtentminnotran: As MGtentmin, but transient behavior is neglected. The input number p in [0, 1] is the last percentage of the solution considered.

tentvideonotran: Video of the evolution of the map given by MGtentminnotran while the parameter α is varying in the input interval [α1, α2].

MGtentnotran2: The critical points M_n considered are the minima of the x(t) coordinate lower than the input bound l, in the two-dimensional projection of the strange attractor given by MGattractor2D. This function plots the critical point M_n as a function of M_{n-1}.

MGtentnotran5: The critical points M_n considered are the points with x(t) coordinate greater than the input bound l and such that the x(t) coordinate of the following point (always in the projection of the strange attractor given by MGattractor2D) is lower than the bound l. Basically, this function detects when the x(t) coordinate of the projection of the attractor crosses the bound l. This function plots the critical point M_n as a function of M_{n-1}.
