Chaos, Solitons & Fractals ( IF 7.8 ) Pub Date : 2021-01-23 , DOI: 10.1016/j.chaos.2021.110688 Diogo Ricardo da Costa , Julia G.S. Rocha , Luam S. de Paiva , Rene O. Medrano-T
In this paper we study a logistic-like and Gauss coupled maps to investigate the period-adding phenomenon, where infinite sets of periodicity () form a sequence in planar parameter spaces, such that, the periodicity of adjacent elements differ by a same constant () in the whole sequence (). 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.
中文翻译:
类似于Logistic和高斯的耦合地图:增周期级联的诞生
在本文中,我们研究了类似logistic的图和高斯耦合图,以研究周期增加现象,其中无限周期的集合()在平面参数空间中形成一个序列,以使相邻元素的周期性相差相同的常数()在整个序列中)。我们描述了从等规闭域形成此序列的完整机制。改变控制参数,在该区域中会产生无限不同的环形环状,从而促进了混沌区域。在这种环境下,出现了几组复杂的周期性,它们按照周期相加的顺序对齐,这是出现在各种非线性动力学系统中的常见情况。应用极端轨道理论可以阐明整个过程。