@article{f50f6f5089b14303b620e146492b408c,
title = "An algorithmic approach to small 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 one to transform the considered differential systems to the normal form 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 and 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 = "Funding Information: Huang's work is partially supported by China Scholarship Council (#201806020128). Yap's work is partially supported by NSF Grants #CCF-1423228 and #CCF-1564132, and also a Chinese Academy of Science (Beijing) President's International Fellowship Initiative (2018), and Beihang International Visiting Professor Program No. Z2018060. The first author is grateful to Professor Dongming Wang for his encouragement and helpful suggestions, and to Professor Chee Yap for inviting him to visit NYU Courant. Both authors thank the anonymous referees for their valuable comments on improving the presentation. Funding Information: Huang's work is partially supported by China Scholarship Council (# 201806020128 ). Yap's work is partially supported by NSF Grants # CCF-1423228 and # CCF-1564132 , and also a Chinese Academy of Science (Beijing) President's International Fellowship Initiative (2018), and Beihang International Visiting Professor Program No. Z2018060 . The first author is grateful to Professor Dongming Wang for his encouragement and helpful suggestions, and to Professor Chee Yap for inviting him to visit NYU Courant. Both authors thank the anonymous referees for their valuable comments on improving the presentation. Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",
year = "2023",
month = mar,
day = "1",
doi = "10.1016/j.jsc.2020.09.001",
language = "English (US)",
volume = "115",
pages = "492--517",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
publisher = "Academic Press Inc.",
}