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Oscillatory modes in a nonlinear second-order differential equation with delay |
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| Authors: | U. an der Heiden A. Longtin M. C. Mackey J. G. Milton R. Scholl |
| Affiliation: | (1) Institut für Mathematik, UniversitÄt Witten/Herdecke, Stockumer Strasse 10, D-5810 Witten, F.R.G.;(2) Department of Physics, McGill University, H3A 2T8 Montréal, Québec, Canada;(3) Center for Nonlinear Dynamics in Physiology and Medicine, McGill University, H3G 1Y6 Montréal, Québec, Canada;(4) Department of Physiology, McGill University, H3G 1Y6 Montréal, Québec, Canada;(5) Department of Neurology, The University of Chicago Hospitals, 60637 Chicago, Illinois |
| Abstract: | Solution properties of the nonlinear second-order delay-differential equation x(t)=–ax(t)+f[x(t–  )] are studied wheref is a piecewise constant function which mimics negative feedback. We show that the solutions can be obtained by a simple geometrical construction which, in principle, can be implemented using a ruler and a compass. Analytical results guarantee the existence and stability properties of limit cycle solutions. Computer-aided constructions reveal a remarkable richness of different types of dynamical behaviors including a variety of unconventional bifurcation schemes. |
| Keywords: | Nonlinear differential equations of second order with deviating argument oscillations periodic solutions |
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