Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation

Abstract

We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form $x^{\prime }(t)=f(x(t-\tau ),x(t))$. As an application, we give a computer assisted proof of the existence of two attracting periodic orbits (before and after the first period-doubling bifurcation) in the Mackey-Glass equation.

References in corpus (1)

• Computer-assisteed proof of a periodic solution in a non-linear feedback DDE

Cited by in corpus (2)

• Traveling wave solutions for the FPU chain: a constructive approach
• High-order Lohner-type algorithm for rigorous computation of Poincaré maps in systems of Delay Differential Equations with several delays