Analysis of the existence of memory phenomena in model heterostructures based on doped ferrite La0.5Sr0.5Fe0.75Al0.2Ni0.05O3-delta with a perovskite structure has been carried out. It was demonstrated that one 5-10 μm thick ferrite layer sandwiched between Pt and Ni electrodes exhibits an analog memristor behavior. Under positive polarity, this heterostructure shows a smooth increase in electrical conductivity, with an opposite effect under negative polarity. Such phenomena are presumably associated with changing local concentrations of oxygen vacancies due to their drift in the electric field. Since lanthanum-strontium ferrites are sufficiently tolerant with respect to oxygen non-stoichiometry variations, no dendrite growth due to reductive decomposition is observed. The current vs. voltage dependencies display a strong nonlinearity resulting from the Poole--Frenkel effect, namely, a decrease in the activation energy of electron holes trapped on oxygen vacancies. In addition to the Poole--Frenkel effect, pre-exponential factor of the conductivity vs. temperature dependence also increases under electric field, indicating an increase in the effective electron-hole mobility. Keywords: perovskite, lanthanum-strontium ferrites, memory effects, nonlinear electronic transport, memristors.