Response of an oscillatory differential delay equation to a single stimulus.
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.
Departments of Physiology, Physics and Mathematics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6, Canada. michael.mackey@mcgill.ca.
Michael C
MC
Mackey
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland.
Marta
M
Tyran-Kamińska
Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany.
Hans-Otto
HO
Walther
D003627:Data Interpretation, Statistical; D008962:Models, Theoretical
34 K 27; 34 K 99; 92 B 25; 92 C 45