The analysis of the periodic orbit for a delay differential equation

In this thesis, stability of limit cycle solutions of the Mackey-Glass delay differential equation are analyzed. For a given set of parameter values, the T-Period orbit is calculated and the stability of that T-Period orbit is analyzed. As one of the parameters in the equation is varied, a family of T-Period orbits is generated and at a critical value of that parameter that T-Period orbit loses its stability to a 2T-Periodic orbit.