Magneto-rotational evolution of neutron stars with hysteresis effect and fallback

In recent years, accreting neutron stars (NSs) in X-ray binary systems in supernova remnants have been discovered. They are a puzzle for the standard magneto-rotational evolution of NSs, as their age ($\lesssim 10^5$ years) is much less than expected duration of the preceding Ejector and Propeller stages. To explain such systems, we consider rotational evolution of NSs with fallback accretion and asymmetry in direct/backward transitions between Ejector and Propeller stages. It is shown that at certain values of the initial period and the magnetic field, a young neutron star may not enter the Ejector stage during its evolution.