@inproceedings{8eb94699be194be481bcd62bd6864776,
title = "An algorithmic approach to limit cycles of nonlinear differential systems: The averaging method revisited",
abstract = "This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging method. The first algorithm allows to transform the considered differential systems to the normal formal of averaging. Here, we restricted the unperturbed term of the normal form of averaging to be identically zero. The second algorithm is used to derive the computational formulae of the averaged functions at any order. The third algorithm is based on the first two algorithms that determines the exact expressions of the averaged functions for the considered differential systems. The proposed approach is implemented in Maple and its effectiveness is shown by several examples. Moreover, we report some incorrect results in published papers on the averaging method.",
keywords = "Algorithmic approach, Averaging method, Center, Limit cycle, Nonlinear differential systems",
author = "Bo Huang and Chee Yap",
note = "Publisher Copyright: {\textcopyright} 2019 Association for Computing Machinery.; 44th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2019 ; Conference date: 15-07-2019 Through 18-07-2019",
year = "2019",
month = jul,
day = "8",
doi = "10.1145/3326229.3326234",
language = "英语",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery ",
pages = "211--218",
booktitle = "ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation",
address = "美国",
}