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

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  • Muhammad Marwan
  • Gauhar Ali
  • Ramla Khan
  • Chun-Biao Li

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.

Suggested Citation

  • Muhammad Marwan & Gauhar Ali & Ramla Khan & Chun-Biao Li, 2022. "Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System," Complexity, Hindawi, vol. 2022, pages 1-14, July.
    • Handle: RePEc:hin:complx:3505634
    DOI: 10.1155/2022/3505634
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