Chaos in fractional and integer order NSG systems

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.