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Chaos in fractional and integer order NSG systems

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journal contribution
posted on 28.01.2017 by S. Hassan HosseinNia, R.L. Magin, B.M. Vinagre
The nuclear spin generator (NSG) is a high-frequency oscillator that generates and controls the oscillations of the precessional motion of a nuclear magnetization vector in a magnetic field. This nonlinear system was first described by S. Sherman in 1963, and exhibits a wide variety of chaotic behavior, but it is not as well studied as the classic Lorenz chaotic system. In this paper, chaos in the integer order nuclear spin generator system is reviewed. In addition, using fractional order stability analysis, the chaotic behavior of the fractional order NSG (FNSG) is studied. The numerical results are obtained using the Adams–Bashforth–Moulton algorithm encoded in the fde12 Matlab function. In order to confirm the numerically demonstrated chaotic behavior in the nuclear spin generator, we prepared a bifurcation diagram. The phase portrait of the FNSG is also depicted for different fractional orders to show the overall chaotic behavior of the system. These results are also verified using bifurcation analysis. Our results demonstrate a modulating effect on chaos as the fractional order decreases, which could be used to improve the design of the controller in the NSG model. This work also demonstrates how the fractional order model extends the dynamic behavior of the NSG system.

Funding

☆ This study was supported in part by NIH/NIBIB Grant EB007537 awarded to Richard L. Magin and by the Government of Extremadura Grant GR10157 awarded to S. Hassan HosseinNia and Blas M. Vinagre.

History

Publisher Statement

This is the copy of an article published in Signal Processing © 2014 Elsevier Publications. http://dx.doi.org/10.1016/j.sigpro.2014.06.021

Publisher

Elsevier

issn

ESSN:0165-1684

Issue date

03/07/2014

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