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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Computational and Graphical Approach to Analyze the Dynamic Wavelet Correlation among Components of a Nonlinear Dynamical System

Journal of Applied Nonlinear Dynamics 12(4) (2023) 757--766 | DOI:10.5890/JAND.2023.12.009

Josu\'e M. Polanco-Mart\'inez

GECOS, IME, University of Salamanca, 37007 Salamanca, Spain

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Abstract

An innumerable number of phenomena that take place in nature can be represented as dynamical systems, which in many cases are not linear. One of the common tasks performed in the study of these systems is to analyse through time and frequency the relationships among their components. In this work, we present, discuss, and extend for the first time in the study of nonlinear dynamical systems, a mathematical and computational tool, the wavelet local multiple correlation (WLMC) to analyse quantitatively and visually the behaviour among components of nonlinear dynamical system. The Lorenz system is used as a case study. The WLMC analysis presented shows that the WLMC is able to capture the most relevant periodic and chaotic dynamics of the Lorenz system as well as the ``dominant'' components of this dynamical system. These results confirm that the WLMC is an adequate mathematical tool to analyse nonlinear and chaotic dynamical systems with multiple components.

Acknowledgments

The author acknowledges to the SEPE (Spanish Public Service of Employment) and the Junta de Castilla y Le\'on, and the European Regional Development Fund (Grant CLU-2019-03) for partial funding support.

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