Abstract
A symbolic computation scheme and its corresponding Maple program are developed to compute the normal form for the Hopf bifurcation in a neutral delay differential equation. In the symbolic computation scheme, the neutral delay differential equation is considered as an ordinary differential equation in an appropriate infinite-dimensional phase space so that both center manifold reduction and normal form computation can be simultaneously conducted without computing center manifold beforehand. The Maple program is proved to provide an easy way to compute the normal form of the neutral delay differential equation automatically by only inputting some basic information of the equation. As an illustrative example, the application of the Maple program to a container crane with a delayed position feedback control is given. The results reveal that the normal form obtained by using the center manifold reduction and the normal form computation is in a full agreement with the result derived by applying the method of multiple scales. Moreover, numerical analysis is presented to validate the analytical results.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
