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Dynamical Properties for a Unified Class of One-Dimensional Discrete Maps

Author

Listed:
  • J. Alberto Conejero

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain)

  • Carlos Lizama

    (Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 9170022, Chile)

  • David Quijada

    (Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 9170022, Chile)

Abstract

Currently, despite advances in the analysis of dynamical systems, there are still doubts about the transition between both stable and chaotic behaviors. In this research, we will explain the transition of a system that develops between two dynamic systems that have already been studied: the classical logistic model and a new chaotic system. This research addresses the study of the transition of both the system and its behaviors using computational techniques, where cobweb diagrams, time series, bifurcation diagrams, and even a graphical visualization for the maximum Lyapunov exponent will be visualized. Using a graphical and numerical methodology, bifurcation points were identified that revealed the transition of behaviors at different points. This resulted in a deep understanding of the dynamics of the system, thus highlighting the importance of incorporating computational analysis in dynamic systems, which greatly contributes to the efficient modeling of natural phenomena.

Suggested Citation

  • J. Alberto Conejero & Carlos Lizama & David Quijada, 2025. "Dynamical Properties for a Unified Class of One-Dimensional Discrete Maps," Mathematics, MDPI, vol. 13(3), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:518-:d:1583281
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