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.
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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|Item Type:||Journal Article|
|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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