# Linear estimate of the number of limit cycles for a class of non-linear systems

Zhang, Tonghua, Tade, Moses O., & Tian, Yu-Chu
(2007)
Linear estimate of the number of limit cycles for a class of non-linear systems.
*Chaos, Solitons and Fractals*, *31*(4), pp. 804-810.

## Abstract

A dynamic system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for general non-linear dynamical systems. In this paper, we investigated a class of non-linear systems under perturbations. We proved that the upper bound of the number of zeros of the related elliptic integrals of the given system is 7n + 5 including multiple zeros, which also gives the upper bound of the number of limit cycles for the given system.

Impact and interest:

**Citation counts** are sourced monthly from **Scopus** and **Web of Science®** citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the **Google Scholar™** indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

**125**since deposited on 29 Jan 2008

**7**in the past twelve months

**Full-text downloads** displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: | 12245 |
---|---|

Item Type: | Journal Article |

Refereed: | Yes |

DOI: | 10.1016/j.chaos.2005.10.029 |

ISSN: | 0960-0779 |

Subjects: | Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301) Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109) |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology |

Copyright Owner: | Copyright 2007 Elsevier |

Copyright Statement: | Reproduced in accordance with the copyright policy of the publisher. |

Deposited On: | 29 Jan 2008 |

Last Modified: | 29 Feb 2012 13:33 |

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page