Special Session 81: 

Fixed point approach to state dependent delay maps: theory and numerical implementation

Vincent NAUDOT
Florida Atlantic University
USA
Co-Author(s):    Jay-Mireles James, Vincent Naudot
Abstract:
In this work we develop a fixed-point method to compute the solutions of phase dependent delay differential equations with (or without) friction. We develop a formulation for the associated Cauchy problem and under appropriate assumptions, obtain the existence of forward iterates of the so called Stroboscopic map. The proof is constructive and leads to numerical procedures which we implement for some illustrative examples.