A Complete Bifurcation Set of Chenciner Bubbles

Munehisa SEKIKAWA  Naohiko INABA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.12   pp.2719-2722
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2719
Type of Manuscript: LETTER
Category: Nonlinear Problems
Keyword: 
invariant torus,  Arnol'd resonance web,  Chenciner bubbles,  

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Summary: 
This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.