Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
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 fraction...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/3505634 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563393811185664 |
|---|---|
| author | Muhammad Marwan Gauhar Ali Ramla Khan |
| author_facet | Muhammad Marwan Gauhar Ali Ramla Khan |
| author_sort | Muhammad Marwan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f25cad6045784d29bf92d93791331f0c |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f25cad6045784d29bf92d93791331f0c2025-02-03T01:20:19ZengWileyComplexity1099-05262022-01-01202210.1155/2022/3505634Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical SystemMuhammad Marwan0Gauhar Ali1Ramla Khan2College of Mathematics and Computer ScienceDepartment of MathematicsSchool of Environment Earth and Ecosystem Sciences (EEES) SchoolThis 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.http://dx.doi.org/10.1155/2022/3505634 |
| spellingShingle | Muhammad Marwan Gauhar Ali Ramla Khan Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System Complexity |
| title | Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System |
| title_full | Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System |
| title_fullStr | Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System |
| title_full_unstemmed | Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System |
| title_short | Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System |
| title_sort | existence of solution and self exciting attractor in the fractional order gyrostat dynamical system |
| url | http://dx.doi.org/10.1155/2022/3505634 |
| work_keys_str_mv | AT muhammadmarwan existenceofsolutionandselfexcitingattractorinthefractionalordergyrostatdynamicalsystem AT gauharali existenceofsolutionandselfexcitingattractorinthefractionalordergyrostatdynamicalsystem AT ramlakhan existenceofsolutionandselfexcitingattractorinthefractionalordergyrostatdynamicalsystem |