Marshall University Math Colloquium

November 5, 2004

“Time scale calculus and dynamical systems”

Kelli Hall and Elizabeth Duke

Marshall University

Abstract

In his 1988 Ph. D. dissertation, Stefan Hilger united continuous and discrete calculus under one calculus system: time-scale calculus. Employing the delta or Hilger derivative, time-scale calculus derives its beauty from the ability to perform on a "mixed" domain, which combines discrete and continuous data sets. Hilger's calculus relies on the idea that we can use the same differentiation and integration systems and change only the time scale from discrete (or "isolated") to continuous (or "dense") and vice versa, rather than changing the calculus system. This talk examines the connection between Hilger's work and the field of dynamical systems by exploring the possibilities for using time scales to shed light on the gap between solutions of the logistic equation in difference and differential calculus. We draw this parallel through an example, which models population with the logistic equation.