<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The paper proposes an original numerical criterion for the duration analysis of non-chaotic transients based on the Euclidean norm of a properly defined vector. For this purpose, transient trajectories, prior to their entering a small neighbourhood of the limit cycle, are used. The vector has been defined with its components constituting the lengths of the sections, which connect the origin of the coordinate system with appropriately determined transient trajectory points. The norm of the vector for the analysis of non-chaotic transients has also been applied. As an assessment criterion of transients, the convergence of the norm to small neighbourhood of the limit cycle with the assumed accuracy is used. The paper also provides examples of the application of this criterion to the Van der Pol oscillators in the case of periodic oscillations.</p>
</abstract>

The paper proposes an original numerical criterion for the duration analysis of non-chaotic transients based on the Euclidean norm of a properly defined vector. For this purpose, transient trajectories, prior to their entering a small neighbourhood of the limit cycle, are used. The vector has been defined with its components constituting the lengths of the sections, which connect the origin of the coordinate system with appropriately determined transient trajectory points. The norm of the vector for the analysis of non-chaotic transients has also been applied. As an assessment criterion of transients, the convergence of the norm to small neighbourhood of the limit cycle with the assumed accuracy is used. The paper also provides examples of the application of this criterion to the Van der Pol oscillators in the case of periodic oscillations.

Numerical Criterion for the Duration of Non-Chaotic Transients in ODEs

Lomza State University of Applied Sciences

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Numerical Criterion for the Duration of Non-Chaotic Transients in ODEs"}

The paper proposes an original numerical criterion for the duration analysis of non-chaotic transients based on the Euclidean norm of a properly defined...

Numerical Criterion for the Duration of Non-Chaotic Transients in ODEs

Published Online: Nov 15, 2022

Page range: 388 - 392

Received: Aug 10, 2022

Accepted: Oct 10, 2022

DOI: https://doi.org/10.2478/ama-2022-0046

Keywords
numerical criterion, non-chaotic transients, limit cycle, ODEs systems, Van der Pol oscillator

© 2022 Ryszard Szczebiot et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Numerical Criterion for the Duration of Non-Chaotic Transients in ODEs

Published Online: Nov 15, 2022

Page range: 388 - 392

Received: Aug 10, 2022

Accepted: Oct 10, 2022

DOI: https://doi.org/10.2478/ama-2022-0046

Keywordsnumerical criterion, non-chaotic transients, limit cycle, ODEs systems, Van der Pol oscillator

© 2022 Ryszard Szczebiot et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
numerical criterion, non-chaotic transients, limit cycle, ODEs systems, Van der Pol oscillator