Multiple Scales without Center Manifold Reductions for Delay Differential Equations near Hopf Bifurcations |
| |
Authors: | Das S. L. Chatterjee A. |
| |
Affiliation: | (1) Mechanical Engineering Department, Indian Institute of Science Bangalore, 560012, India |
| |
Abstract: | We study small perturbations of three linear Delay DifferentialEquations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reductionas a first step. We demonstrate that the method of multiple scales, onsimply discarding the infinitely many exponentially decaying components of the complementary solutionsobtained at each stage of the approximation,can bypass the explicit center manifold calculation.Analytical approximations obtained for the DDEs studied closely matchnumerical solutions. |
| |
Keywords: | delay differential equation multiple scales Hopf bifurcation center manifold |
本文献已被 SpringerLink 等数据库收录! |
|