Existence of Unstable Manifolds for a Certain Class of Delay Differential Equations
Date
2002-04-01
Authors
Krishnan, Hari P.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We prove a theorem for unstable manifolds in a differential equation with a state-dependent delay. Although the equation cannot be formally linearized, we find an associated linear delay equation whose dynamics are qualitatively similar near the unstable manifold. Our proof relies upon estimates of the derivative of a trajectory on the unstable manifold near equilibrium.
Description
Keywords
Invariant manifolds, Functional differential equations
Citation
Krishnan, H. P. (2002). Existence of unstable manifolds for a certain class of delay differential equations. <i>Electronic Journal of Differential Equations, 2002</i>(32), pp. 1-13.
Rights
Attribution 4.0 International