Bifurcating periodic solution for a class of first-order nonlinear delay differential equation after Hopf bifurcation
Author(s)
Author(s)
Guo, Z.
Liu, Y. C.
Yang, H. X.
Date Issued
2012
Publisher
Elsevier
Journal
Applied Mathematical Modelling
Volume
36
Issue
10
Start page
4837
End page
4846
Abstract
In this paper, we predict the accurate bifurcating periodic solution for a general class of first-order nonlinear delay differential equation with reflectional symmetry by constructing an approximate technique, named residue harmonic balance. This technique combines the features of the homotopy concept with harmonic balance which leads to easy computation and gives accurate prediction on the periodic solution to the desired accuracy. The zeroth-order solution using just one Fourier term is applied by solving a set of nonlinear algebraic equations containing the delay term. The unbalanced residues due to Fourier truncation are considered iteratively by solving linear equations to improve the accuracy and increase the number of Fourier terms of the solutions successively. It is shown that the solutions are valid for a wide range of variation of the parameters by two examples. The second-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration. Moreover, the residue harmonic balance method works not only in determining the amplitude but also the frequency of the bifurcating periodic solution. The method can be easily extended to other delay differential equations.
SFU Affiliated Publication
No
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