Periodic solutions of singularly perturbed delay equations |
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Authors: | Jack K Hale Wenzhang Huang |
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Institution: | (1) Center for Dynamic Systems & Nonlinear Studies, Georgia Institute of Technology, 30332-0190 Atlanta, GA;(2) Department of Mathematical Sciences, University of Alabama in Huntsville, 35899 Huntsville, AL, USA |
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Abstract: | We consider a general class of singularly perturbed delay differential systems depending on a singular parameter and another parameter . For =0, the equation defines a mapT which undergoes a generic period doubling at =0. If the bifurcation is supercritical (subcritical), these period two points define a stable period two square wave (unstable period two pulse wave). We give conditions on the vector field such that there is a sectorS in the , plane such that there is a unique periodic orbit if the parameters are inS, the orbit is stable (unstable) if the period doubling bifurcation is supercritical (subcritical) and approaches the square (pulse) wave as 0.Partially supported by NSF and DARPA. |
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