title: Analytical and experimental study of two delay-coupled excitable units.
abstract: We investigate the onset of time-periodic oscillations for a system of two identical delay-coupled excitable (nonoscillatory) units. We first analyze these solutions by using asymptotic methods. The oscillations are described as relaxation oscillations exhibiting successive slow and fast changes. The analysis highlights the determinant role of the delay during the fast transition layers. We then study experimentally a system of two coupled electronic circuits that is modeled mathematically by the same delay differential equations. We obtain quantitative agreements between analytical and experimental bifurcation diagrams.
authors.affiliation: Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, C. P. 231, 1050 Bruxelles, Belgium.
authors.forename: Lionel
authors.initials: L
authors.lastname: Weicker
authors.affiliation: Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, C. P. 231, 1050 Bruxelles, Belgium.
authors.forename: Thomas
authors.initials: T
authors.lastname: Erneux
authors.affiliation: Applied Physics Research Group (APHY), Vrije Universiteit Brussel, 1050 Brussel, Belgium.
authors.forename: Lars
authors.initials: L
authors.lastname: Keuninckx
authors.affiliation: Applied Physics Research Group (APHY), Vrije Universiteit Brussel, 1050 Brussel, Belgium.
authors.forename: Jan
authors.initials: J
authors.lastname: Danckaert