An algorithmic approach to limit cycles of nonlinear differential systems: The averaging method revisited

Bo Huang, Chee Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation
PublisherAssociation for Computing Machinery
Pages211-218
Number of pages8
ISBN (Electronic)9781450360845
DOIs
StatePublished - Jul 8 2019
Event44th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2019 - Beijing, China
Duration: Jul 15 2019Jul 18 2019

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference44th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2019
CountryChina
CityBeijing
Period7/15/197/18/19

Fingerprint

Averaging Method
Differential System
Limit Cycle
Nonlinear Systems
Averaging
Maple
Continuous System
Normal Form
Bifurcation
Transform
Zero
Term

Keywords

  • Algorithmic approach
  • Averaging method
  • Center
  • Limit cycle
  • Nonlinear differential systems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Huang, B., & Yap, C. (2019). An algorithmic approach to limit cycles of nonlinear differential systems: The averaging method revisited. In ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation (pp. 211-218). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). Association for Computing Machinery. https://doi.org/10.1145/3326229.3326234

An algorithmic approach to limit cycles of nonlinear differential systems : The averaging method revisited. / Huang, Bo; Yap, Chee.

ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2019. p. 211-218 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Huang, B & Yap, C 2019, An algorithmic approach to limit cycles of nonlinear differential systems: The averaging method revisited. in ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, Association for Computing Machinery, pp. 211-218, 44th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2019, Beijing, China, 7/15/19. https://doi.org/10.1145/3326229.3326234
Huang B, Yap C. An algorithmic approach to limit cycles of nonlinear differential systems: The averaging method revisited. In ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery. 2019. p. 211-218. (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/3326229.3326234
Huang, Bo ; Yap, Chee. / An algorithmic approach to limit cycles of nonlinear differential systems : The averaging method revisited. ISSAC 2019 - Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery, 2019. pp. 211-218 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).
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