The vortex dynamics and the specific heat of a type II superconducting system with quasi-periodic geometry is studied theoretically for different values of interaction parameters using the numerical simulation technique, where the vortex-vortex interaction potential is considered in the form of the modified Bessels function of first kind. The dynamics of the system is analysed by phase space trajectories of the vortex for both high and low values as well as for both high and low mismatch of vortex-vortex and vortex-pinning interaction parameters. The specific heat variation with temperature is analysed statistically for different values of interaction parameters. It is observed that for low values and lower mismatch of interaction parameters, the system is highly chaotic and shows a bifurcation pattern similar to Hopf bifurcation. The specific heat also shows a highly divergent character in this situation. However for high values and higher mismatch, the superconducting system tends to be a very regular one. The trajectory of the vortices will also be very stable in this situation. Similar situations are also observed respectively for low and high values of the quasi-periodic parameter.
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