An algorithmic approach to small limit cycles of nonlinear differential systems: The averaging method revisited
| Autor: | Bo Huang, Chee Yap |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Maple
Algebra and Number Theory 010102 general mathematics Zero (complex analysis) Order (ring theory) 010103 numerical & computational mathematics engineering.material 01 natural sciences Term (time) Computational Mathematics Nonlinear system Limit cycle engineering Applied mathematics Limit (mathematics) 0101 mathematics Bifurcation Mathematics |
| Zdroj: | Journal of Symbolic Computation. 115:492-517 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2020.09.001 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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