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A Complete Bifurcation Set of Chenciner Bubbles
Munehisa SEKIKAWA Naohiko INABA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2015/12/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Nonlinear Problems
invariant torus, Arnol'd resonance web, Chenciner bubbles,
Full Text: PDF(577.8KB)>>
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.