Hysteresis in the behavior of a long periodically modulated Josephson junction in a magnetic field for not small values of the pinning parameter

The magnetization curve for a long periodically modulated Josephson junction is calculated using the approach based on analysis of the continuous change in the configuration in the direction of the decrease in the Gibbs potential upon cyclic variation of the external magnetic field for not small values of pinning parameter $I$. It is shown that unlike in the case of small $I$, when the hysteresis loop is a part of a certain universal curve, the segments of the loops corresponding to a decrease in $h$ in the first and second quadrants (and symmetric to them) pass below the universal loop, the degree of deviation increasing with pinning parameter $I$. The properties of the hysteresis loops are considered for various amplitudes of the magnetic field variation on the basis of analysis of vortex configurations.