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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 66, Issue 2

Issues

Note on a parameter switching method for nonlinear ODEs

Marius-F. Danca
  • Department of Mathematics and Computer Science Emanuel University of Oradea 410597 Oradea ROMANIA Romanian Institute for Science and Technology Str. Cireilor 29 400487 Cluj-Napoca ROMANIA
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/ Michal Fečkan
  • Department of Mathematical Analysis and Numerical Mathematics Comenius University Mlynská dolina 842 48 Bratislava SLOVAKIA Mathematical Institute Slovak Academy of Sciences Štefánikova 49 814 73 Bratislava SLOVAKIA
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Published Online: 2016-07-05 | DOI: https://doi.org/10.1515/ms-2015-0148

Abstract

In this paper we study analytically a parameter switching (PS) algorithm applied to a class of systems of ODE, depending on a single real parameter. The algorithm allows the numerical approximation of any solution of the underlying system by simple periodical switches of the control parameter. Near a general approach of the convergence of the PS algorithm, some dissipative properties are investigated and the dynamical behavior of solutions is investigated with the Lyapunov function method. A numerical example is presented.

MSC 2010: Primary 34K28; Secondary 34C29, 37B25, 34H10

Keywords: numerical approximation of solutions; averaging method; Lyapunov function; chaos control; anticontrol

Dedicated to Professor Anatolij Dvurečenskij on the occasion of his 65th birthday

(Communicated by Jozef Džurina)

M. Fečkan is partially supported by Grants VEGA-MS 1/0071/14 and VEGA-SAV 2/0153/16.

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About the article

Received: 2013-05-27

Accepted: 2014-01-05

Published Online: 2016-07-05

Published in Print: 2016-04-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 2, Pages 439–448, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0148.

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