Wada bifurcations and partially Wada basin boundaries in a two-dimensional cubic map

The partially Wada basin boundaries are referred to the coexistence of Wada points and non-Wada points in the same basin boundary. We demonstrate two types of Wada bifurcations and analyze the transitions from totally Wada basins to partially Wada basins and from totally Wada basins to totally Wada...

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Bibliographic Details
Published in:Physics letters. A 2013-08, Vol.377 (18), p.1274-1281
Main Authors: Zhang, Yongxiang, Luo, Guanwei
Format: Article
Language:English
Subjects:
Basin cell
Basins
Bifurcations
Boundaries
Erosion
Erosion mechanisms
Partially Wada basin boundary
Solid state physics
Two dimensional
Wada bifurcation
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Summary:The partially Wada basin boundaries are referred to the coexistence of Wada points and non-Wada points in the same basin boundary. We demonstrate two types of Wada bifurcations and analyze the transitions from totally Wada basins to partially Wada basins and from totally Wada basins to totally Wada basins in a two-dimensional cubic map. We describe some numerical experiments giving the evidence of partially Wada basin boundaries. Our results show that the basin cell erosion and the basin cell bifurcation can induce the Wada basin boundary metamorphoses. •We give two types of Wada bifurcations in a cubic map.•We report the creation of the partially Wada basin boundaries by a basin cell erosion.•The basin cell bifurcation can induce Wada basin metamorphoses.•The 8-sided basin cell and the 10-sided basin cell are first used to verify the full Wada basin boundaries.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2013.03.027