  The present paper examines the influence of a nonlinear relationship between
the local oxygen-vacancy concentration and the local resistivity on resistive
switching effects in complex oxides. The continuity equation has been used as a
model for the motion of oxygen vacancies when a periodic time-dependent
electrical current is applied. The question of endurance of the switching
cycles is discussed. It is found that nonlinearity of the
resistivity-concentration dependence enhances the endurance.
