Strange Attractors and Optimal Analysis of Chaotic Systems based on Fractal verses Fractional Differential Operators. (3rd September 2022)

• Record Type: Journal Article
• Authors: Abro, Kashif Ali; Atangana, Abdon
• Is Part Of: International journal of modelling & simulation. Volume 42:Number 5(2022)
• Page Start: 716
• Page End: 724
• Publication Date: 2022-09-03
• Subjects: Strange attractors with equilibrium -- mittage-leffler kernel -- numerical simulations -- optimal study for 2D and 3D chaotic; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2021.1966729
• Languages: English
• ISSNs: 0228-6203

Abstract

ABSTRACT: In this paper, role of chaotic systems with perpendicular line equilibrium, line equilibrium, and no-equilibrium is investigated by employing Mittage-Leffler kernel. The fractal-fractionalized mathematical and dynamical models have been observed for quasi-periodicity chaos and hyperchaos as well as simple periodicity chaos and hyperchaos. Each chaotic systems type is simulated on the basis on comparative analysis through Atangana-Baleanu fractal differential operator versus Atangana-Baleanu fractional differential operator. The numerical simulations have been performed by means of Adams-Bashforth-Moulton method for observing the controversial role of chaotic systems on the basis of phase portrait. The nonsingularity associate to the fractal fractional differentiation of Atangana-Baleanu has been introduced. Finally, 3D and 2D phase portraits of chaotic system with perpendicular line equilibrium, line equilibrium and no-equilibrium have been underlined to capture the similarities and differences among the depicted phase portraits parametrically.