Back to ODE: a numerical approach for periodic solutions of delay equations

Delay differential equations (DDEs) generate infinite-dimensional dynamical systems. Anyway, the center manifold theorem guarantees that the “interesting” local dynamics happen entirely in a finite-dimensional subspace. Concerning periodic solutions, this result allows to use techniques that are very similar to those for ODEs and to define concepts like Poincaré maps and Floquet multipliers. I will briefly present a recently developed numerical method (based on pseudospectral discretization) for the numerical analysis of the dynamics and bifurcations of DDEs. This tool is used to obtain numerical examples of dynamical behavior related to limit cycles, and to show how interesting bifurcations can be detected by studying the multipliers of the linearized system.

The seminar is linked to the course Periodic orbits of dynamical systems.