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Title

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

Author(s)

Zhang, Tonghua;  Tade, Moses O.;  Tian, Yu-Chu

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.

Publication type

Journal article

Source

Chaos, Solitons and Fractals, Vol. 31, no. 4 (Feb 2007), pp. 804-810

Publication year

2007

FOR Code(s)

0102 Applied Mathematics

Keyword(s)

Elliptic integrals;  Finite difference method;  Integral equations;  Limit cycles;  Linear estimate;  Multiple zeros;  Nonlinear systems;  Number theory;  Parameter estimation;  Perturbation techniques;  Problem solving

Publisher

Pergamon

ISSN

0960-0779

Publisher URL

http://dx.doi.org/10.1016/j.chaos.2005.10.029

Copyright

Copyright © 2005 Elsevier Ltd. This is the author's version of a work that was accepted for publication in Chaos, Solitons and Fractals. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Chaos, Solitons and Fractals, 31, 4, 2007: 10.1016/j.chaos.2005.10.029.

Full text

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