Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2004 / Article

Open Access

Volume 2004 |Article ID 290953 | https://doi.org/10.1155/S1024123X04311038

Konstantin E. Starkov, "Localization of periodic orbits of autonomous systems based on high-order extremum conditions", Mathematical Problems in Engineering, vol. 2004, Article ID 290953, 14 pages, 2004. https://doi.org/10.1155/S1024123X04311038

Localization of periodic orbits of autonomous systems based on high-order extremum conditions

Received12 Nov 2003
Revised16 Mar 2004

Abstract

This paper gives localization and nonexistence conditions of periodic orbits in some subsets of the state space. Mainly, our approach is based on high-order extremum conditions, on high-order tangency conditions of a nonsingular solution of a polynomial system with an algebraic surface, and on some ideas related to algebraically-dependent polynomials. Examples of the localization analysis of periodic orbits are presented including the Blasius equations, the generalized mass action (GMA) system, and the mathematical model of the chemical reaction with autocatalytic step.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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