Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System

Muhammad Marwan, Gauhar Ali, Ramla Khan and Chun-Biao Li

Complexity, 2022, vol. 2022, 1-14

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:3505634

DOI: 10.1155/2022/3505634

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