Received: 30 January 2024
Accepted: 15 February 2024
Volume 1. Issue 1. Pages 29-30 (2024)
(1) Rida, (2) Shahab Ud-Din Khan
Affiliation:
- Department of Mathematics, Wah Campus, COMSATS University, Islamabad, Pakistan
- Pakistan Tokamak Plasma Research Institute (PTPRI), Islamabad, Pakistan
The distinction between slow and fast dynamos was first drawn by Vainshtein & Zeldovich (1972) in this research; we describe the stretch-twist-fold (STF) fast dynamo, which is the archetype of the elementary models of the process. Basically, stretch-twist-fold is applied in fluid mechanics in aerospace. In space, any fluid can be D-Tracked easily so a magnetic field is required to compel the fluid to be in the same orbit and this method is called STF system. In this work we search the chaotic behavior for the STF system through employment sensitive depends on initial condition by using the software (Matlab) We get sensitive depends on initial (Chaos) by varying the parameter of system. Since the poincare’e-Bendixson theorem precludes the existence of other than steady periodic, attractors in autonomous system defined in one- or two-dimensional manifolds such as the line, the circle, the plane, the sphere, or the torus. Further, we study the chaotic behavior of STF system depend on the definition of (Gulick, 1992). Such as, definition of Lyapunov exponent, Sensitive dependence on initial condition, Chaos, Capacity and fractal dimension, Bifurcation, Bifurcation diagram.
- Salah Ud-Din Khan, Shahab Ud-Din Khan, “Equating heteroclinic orbits in Chen System by using Scaling Logarithm Change Series (SLS) method” Applied Mechanics and Materials Vol. 598. pp 414-417. 2014
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- Shahab Ud-Din Khan, S.Yonglu, Salah Ud-Din Khan, “Stability and Unstability of Chaos in Stretch-Twist- Fold flow (STF)”, Advanced Materials Research, Vols. 631-632, pp 1436-1440, 2013
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- Shahab Ud-Din Khan, S.Yonglu, Salah Ud-Din Khan, “Complex dynamics of continuous-time autonomous chaotic system”, International Journal of Physics and Mathematical Sciences, Vol. 2 (3), pp.108-114, 2012
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- Shahab Ud-Din Khan, S.Yonglu, Salah Ud-Din Khan, “Stability Control of Stretch-Twist-Fold Flow by Using Numerical Methods”, World Journal of Mechanics, Vol. 2 No.6, 334-338, 2012
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The research team show their gratitude and sincere appreciation to Department of Mathematics and Pakistan Tokamak Plasma Research Institute (PTPRI), for support of this research.
- STF System
- Numerical Solution
- MATLAB Program
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We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.