Reproducible bipolar resistive switching has been studied in SiOx-based thin-film memristor structures deposited by magnetron sputtering technique on the TiN/Ti metalized SiO2/Si substrates. It is established that, after electroforming, the structure can be switched between the quasi-ohmic low-resistance state related to silicon chains (conducting filaments) and the high-resistance state with semiconductor-like hopping mechanism of charge transport through the defects in silicon oxide. The switching parameters are determined by a balance between the reduction and oxidation processes that, in turn, are driven by the value and polarity of voltage bias, current, temperature and device environment. The results can be used for the development of silicon-based nonvolatile memory and memristive systems as a key component of future electronics.