Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System. (18th July 2022)

• Record Type: Journal Article
• Authors: Marwan, Muhammad; Ali, Gauhar; Khan, Ramla
• Other Names: Li Chun-Biao Academic Editor.
• Is Part Of: Complexity. Volume 2022(2022)
• Publication Date: 2022-07-18
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2022/3505634
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain.