# 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.

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ID Code: | 12245 |
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Item Type: | Journal Article |

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 |

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