Symbolic computation of normal form for Hopf bifurcation in a retarded functional differential equation with unknown parameters |
| |
Authors: | Li ZhangHuailei Wang Haiyan Hu |
| |
Institution: | a State Key Laboratory of Mechanical Vibration and Strength, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China b School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, People’s Republic of China |
| |
Abstract: | Based on the normal form theory for retarded functional differential equations by Faria and Magalhães, a symbolic computation scheme together with the Maple program implementation is developed to compute the normal form of a Hopf bifurcation for retarded functional differential equations with unknown parameters. Not operating as the usual way of computing the center manifold first and normal form later, the scheme features computing them simultaneously. Great efforts are made to package this task into one Maple program with an input interface provided for defining different systems. The applicability of the Maple program is demonstrated via three kinds of delayed dynamic systems such as a delayed Liénard equation, a simplified drilling model and a delayed three-neuron model. The effectiveness of Maple program is also validated through the numerical simulations of those three systems. |
| |
Keywords: | Delay differential equation Normal form Center manifold Symbolic computation Maple program |
本文献已被 ScienceDirect 等数据库收录! |