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In this work we proposed two detection schemes based on the non-linear properties of the Duffing-Holmes oscillator for the detection of small variations in the damping coefficient. Theoretically, variations in the damping coefficient up to 0.001% with the possibility to be pushed further can be detected based on our model. A potential on-off magnetic sensor suitable for biomedical applications is suggested by implementing these two schemes with Giant Magnetoresistance based magnetic sensors.

In this work, the dynamics of Duffing-Holmes oscillator with fractional order nonlinearity is explored. Basically, a fractional spatial derivative is introduced to the cubic term, and the order of the derivative α is varied between zero and two. The evolution of the dynamics of the system from nonlinear behavior to linear behavior is investigated using multiple tools such as phase portraits, Poincare maps, and bifurcation diagrams. We have demonstrated that as α increases the system can alternate between chaotic and periodic states depending on the parameters setting. However, the overall impact transforms the system into simpler dynamics and eventually causes the chaotic regions to fade out regardless of the system settings. The largest α at which the system still exhibits chaotic behavior is estimated to be around 1.17 and for transient chaos is estimated to be 1.25.

Specimens of Tl-1223 superconducting tapes have been prepared using the powder-in-tube (PIT) method. Effects of gamma irradiation on the structure and transport properties of Tl-1223 tapes have been studied up to a gamma dose of 400 MR. A gradual decrease in the transition temperature and increase in the normal state resistance have been observed. A considerable decrease in the intensities of the major diffraction peaks of the XRD pattern was observed due to gamma irradiation. The I-V data were fitted to the power law V ~ I α (B,T) in which the power exponent α was found to increase gradually with gamma dose. The dependence of α on the temperature was studied and the effect of gamma irradiation on the pinning energy was discussed and explained in terms of the defects introduced on the grain boundaries, weak links, and Josephson junctions.

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