Dynamical properties of the composed Logistic-Gauss map

Luam Silva de Paiva; Julia G S Rocha; Joelson D V Hermes; Matheus Hansen; Ricardo Luiz Viana; Iberê Luiz Caldas; Rene O Medrano-T; Diogo Ricardo da Costa

doi:10.1063/5.0238591

Dynamical properties of the composed Logistic-Gauss map

Chaos. 2025 Jan 1;35(1):013129. doi: 10.1063/5.0238591.

Authors

Luam Silva de Paiva¹, Julia G S Rocha¹, Joelson D V Hermes^{2

3}, Matheus Hansen⁴, Ricardo Luiz Viana⁵, Iberê Luiz Caldas³, Rene O Medrano-T^{1

6}, Diogo Ricardo da Costa^{3

5}

Affiliations

¹ Department of Physics, São Paulo State University-UNESP, Rio Claro, SP 13506-900, Brazil.
² Federal Institute of Education, Science and Technology of South of Minas Gerais-IFSULDEMINAS, Inconfidentes, MG 37576-000, Brazil.
³ Physics Institute, University of São Paulo-USP, São Paulo, SP 05508-090, Brazil.
⁴ Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology, Universidade NOVA de Lisboa, Quinta da Torre, Caparica 2829-516, Portugal.
⁵ Department of Physics, Federal University of Paraná-UFPR, Curitiba, PR 82590-300, Brazil.
⁶ Department of Physics, Federal University of São Paulo - UNIFESP, Diadema, SP 09913-030, Brazil.

PMID: 39792700
DOI: 10.1063/5.0238591

Abstract

This study focuses on the analysis of a unique composition between two well-established models, known as the Logistic-Gauss map. The investigation cohesively transitions to an exploration of parameter space, essential for unraveling the complexity of dissipative mappings and understanding the intricate relationships between periodic structures and chaotic regions. By manipulating control parameters, our approach reveals intriguing patterns, with findings enriched by extreme orbits, trajectories that connect local maximum and minimum values of one-dimensional maps. This theory enhances our perception of structural organization and offers valuable perceptions of the system behaviors, contributing to an expanded understanding of chaos and periodicity in dynamic systems. The analysis reveals Complex Sets of Periodicity (CSP) in the parameter space, characterized by superstable curves that traverse their main bodies. The exploration of different combinations of parameters shows cascades of CSP structures with added periods and are organized based on extreme curves. This investigation offers valuable discoveries of the dynamics of dissipative mappings, opening avenues for future explorations in chaotic systems.