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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.

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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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2 citations in Scopus
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3 citations in Web of Science®

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120 since deposited on 29 Jan 2008
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ID Code: 12245
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 23:33

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