Stability of state-dependent delay differential equations

Felicia Magpantay
Department of Mathematics and Statistics at Queen’s

Abstract

Much of the theory and applications of delay differential equations (DDEs) focuses on constant and time-dependent time delays. How- ever, many delays in physical (e.g. action-at-a-distance electrodynam- ics), biological (e.g. structured population models) and engineering (e.g. automatic position control) systems naturally vary with the state of the system and lead to state-dependent delay differential equations (SDDEs). In this talk I will present some background on the theory and applications of DDEs and SDDEs, and sketch ideas behind how to show the stability of solutions to SDDEs using Lyapunov-Razumikhin methods. Similar techniques can be used to derive bounds on periodic solutions. This is joint work with A.R. Humphries (McGill University).