Stable periodic orbits for the Mackey-Glass equation

Abstract: We consider the classical Mackey-Glass delay differential equation. By letting n go to infinity in the part encapsulating the delayed term, we obtain a limiting hybrid delay equation. We investigate how periodic solutions of this limiting equation are related to periodic solutions of the original MG equation for large n. Then, we establish a procedure for constructing such periodic solutions via forward time integration. Finally, we use rigorous numerics to establish the existence of stable periodic orbits for various parameters of the MG equation. We note that some of these solutions exhibit seemingly complicated dynamics, yet they are stable periodic orbits.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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