Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13030518

Authors: J. Alberto Conejero, Carlos Lizama, David Quijada

Institutions: Universitat Politècnica de València, Universidad de Santiago de Chile

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Fondo Nacional de Desarrollo Científico y Tecnológico