Basins of attraction for a quadratic coquaternionic map. (November 2017)

• Record Type: Journal Article
• Authors: Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana
• Is Part Of: Chaos, solitons and fractals. Volume 104(2017)
• Page Start: 716
• Page End: 724
• Publication Date: 2017-11
• Subjects: Iteration of maps -- Coquaternions -- Attracting cycles -- Basins of attraction; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.09.016
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The dynamics of a quadratic coquaternionic map is studied. Coexistence of five attracting cycles of period eight is established. The basins of attraction of the five attracting 8-cycles are analyzed. The intertwined nature of the basins of attraction is shown. Abstract: In this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here, the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.