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

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.

Automated summary

This paper studies a logistic-like and Gauss coupled maps model to investigate the period-adding phenomenon, revealing the complete process of forming complex sets of period-adding periodicity by changing control parameters in a closed domain of isoperiodicity.