Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus

被引:51
作者
Atangana, Abdon [1 ]
Mekkaoui, Toufik [2 ]
机构
[1] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa
[2] Moulay Univ Meknes, Ismail Fac Sci & Technol, Dept Math, BP 509, Boutalamine, Errachidia, Morocco
关键词
Trinition; Fractal mapping; Chaos; Strange attractors; Ekoung;
D O I
10.1016/j.chaos.2019.08.018
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Human being live in three-dimensional space; they can accurately visualize processes taking place in one, two and three dimensions. Although the set of bi-complex numbers and quaternion have attracted attention of many researchers in physics and related branches, they do not really represent processes taking place in the space where human being are located. We suggested a new set of complex number called "the Trinition". The new set is comprised between complex number with one imaginary part and complex number with three imaginary parts called quaternion/bi-complex numbers. We established a bijection between the new set and the three-dimensional space. We presented some important properties of the new set. We showed that all chaotic attractors in three dimension are simply three-dimensional mapping in the new set. Fewer examples of mapping in such set were presented. A new methodology that can be used to obtain more strange attractors are equally suggested. The methodology combines fractional chaotic models and some fractal mapping within the new set. Some illustrative figures are presented. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码:366 / 381
页数:16
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