Illustrate the Butterfly Effect on the Chaos Rikitake system

Yousof Gholipour, Amin Ramezani, Mahmood Mola

Abstract


This letter presents butterfly effect on a Chaos system. In this letter we want to briefly introduce Chaos Rikitake system and monitor the butterfly effect on this system. In chaos theory, the butterfly effect is the sensitive dependency on initial conditions. For this goal at the first we suppose initiation point and plot it, for base of work, later will apply small change on one item of initiation point and monitor behavior of Rikitake system. At the end we want to reclaim the famous lecture of Edward Lorenz in 1972 “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”. The numerical simulations by use of MATLAB software are given to illustrate the butterfly effect on this system.

Keywords


Chaos; Rikitake system; butterfly effect; initiation point

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References


Ahmad Harb, Nabil Ayoub. (2013). Nonlinear Control of Chaotic Rikitake Two-Disk Dynamo, International Journal of Nonlinear Science. Vol.15 No.1: 45-50.

Denis de Carvalho Braga, Fabio Scalco Dias, Luis Fernando Mello(2010). On the stability of the equilibria of the Rikitake system. Physics Letters. 374: 4316-4320.

Carlos Aguilar-Ibañez, Rafael Martinez-Guerra,Ricardo Aguilar-López, Juan L. Mata-Machuca. (2010). Synchronization and parameter estimations of an uncertain Rikitake system, Physics Letters A 374: 3625–3628.

JOHN H, MATHEWS, W. K. GARDNER (1968). Field Reversals of "Paleomagnetic" Type in Coupled Disk Dynamos. U.S. NAVAL RESEARCHLABORATORY. Washington, D.C. USA, pp.2-5.

Liu Xiao-jun, Li Xian-feng, Chang Ying-xiang, Zhang Jian-gang. (2013). Chaos and Chaos Synchronism of the Rikitake Two-Disk Dynamo. Fourth International Conference on Natural Computation, IEEE computer Society,DOI10.1109/ICNC.2008.706:613-617.

T. Rikitake. (1958). Oscillations of a System of Disk Dynamos. Proc. Cambridge Philos. Soc.54- 89.

U.E. Vincent, R. Guo. (2011). Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller, Physics Letters A 375: 2322–2326.

Yousof Gholipour, Mahmood Moula. (2014). Investigation Stability of Rikitake System. JCET Vol. 4 Iss. 1 January: 82-85.




DOI: https://doi.org/10.11591/eei.v3i4.292

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Bulletin of Electrical Engineering and Informatics (BEEI)
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