Affiliation of Author(s):航空学院
Journal:ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
Key Words:neutral delay differential equation Hopf bifurcation center manifold reduction normal form method of multiple scales implicit differential equations
Abstract:Hopf bifurcation analysis is conducted on a scalar implicit Neutral Delay Differential Equation (NDDE) by means of the extension of two analytical methods: 1) center manifold reduction combined with normal form theory; 2) method of multiple scales. The modifications of the classical algorithms originally developed for explicit differential equations lead to the same algebraic results, which are further confirmed by numerical simulations. It is shown that the generalizations of these regular normal form calculation methods are useful for the local nonlinear analysis of implicit NDDEs where the explicit formalism is typically not accessible and the existence and uniqueness of solutions around the equilibrium are only assumed together with the existence of a smooth local center manifold.
ISSN No.:1417-3875
Translation or Not:no
Date of Publication:2018-01-01
Co-author:Stepan, Gabor
Correspondence Author:张丽