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Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

Das, SL and Chatterjee, A (2002) Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations. In: Nonlinear Dynamics, 30 (4). pp. 323-335.

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Abstract

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Keywords: Delay differential equation;multiple scales;Hopf bifurcation; center manifold.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 21 Jul 2011 07:02
Last Modified: 21 Jul 2011 07:02
URI: http://eprints.iisc.ernet.in/id/eprint/39294

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