Limit cycles,tori, and complex dynamics in a second-order differential equation with delayed negative feedback |
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| Authors: | Sue Ann Campbell Jacques Bélair Toru Ohira John Milton |
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| Institution: | (1) Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montréal, Québec, Canada;(2) Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada;(3) Centre de recherches mathématiques, Université de Montréal, Montréal, Québec, Canada;(4) Department of Physics, The University of Chicago, Chicago, Illinois;(5) Department of Neurology, The University of Chicago, Chicago, Illinois;(6) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada;(7) Sony Computer Science Laboratory Inc., Tokyo, Japan;(8) Département de mathématiques et de statistique, Université de Montréal, C.P. 6128-A, H3C 3J7 Montréal, Québec, Canada |
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| Abstract: | We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined. |
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| Keywords: | Time delay negative feedback Hopf bifurcations center manifold invariant tori |
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