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

J. Alberto Conejero (), Carlos Lizama and David Quijada
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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

Mathematics, 2025, vol. 13, issue 3, 1-17

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.

Keywords: logistic map; chaos; cobweb plot; time series plots; bifurcation diagrams; maximal Lyapunov exponent; transition points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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