Logistic-like and Gauss coupled maps: The born of period-adding cascades

Author(s)

da Costa, Diogo Ricardo ^{[1, 2]} ; Rocha, Julia G. S. ^[3] ; de Paiva, Luam S. ^[3] ; Medrano-T, Rene O. ^{[3, 4]}

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, BR-05508090 Sao Paulo - Brazil

^[2] State Univ Ponta Grossa UEPG, Postgrad Program Sci Phys, BR-84030900 Ponta Grossa, Parana - Brazil

^[3] Univ Estadual Paulista, UNESP, Dept Fis, Inst Geociencias & Ciencias Exatas, Campus Rio Claro, Av 24A, 1515, BR-13506900 Rio Claro, SP - Brazil

^[4] Univ Fed Sao Paulo, UNIFESP, Dept Fis, Campus Diadema, R Sao Nicolau 210, BR-09913030 Diadema, SP - Brazil

• Document type: Journal article
• Source: CHAOS SOLITONS & FRACTALS; v. 144, MAR 2021.
• Web of Science Citations: 1

Abstract

In this paper we study a logistic-like and Gauss coupled maps to investigate the period-adding phenomenon, where infinite sets of periodicity (p) form a sequence in planar parameter spaces, such that, the periodicity of adjacent elements differ by a same constant (rho) in the whole sequence (p(i+1) - p(i) = rho). We describe the complete mechanism that form this sequence from a closed domain of isoperiodicity. Changing a control parameter, infinite different periodicities ring-shaped take place in this domain promoting regions of chaoticity. In this environment several complex sets of periodicity arise aligning themselves in sequences of period-adding, which is a common scenario that appears in a great variety of nonlinear dynamical systems. The complete process is unraveled by applying the theory of extreme orbits. (C) 2021 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 20/02415-7 - StatGraph 2.0 and Massive Open Online Course (MOOC)
• Grantee: Diogo Ricardo da Costa
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants