The operating principle of resistive random access memories (RRAMs) relies on the distribution of ionic species and their influence on the electron transport. Taking into account that formation and annihilation of conducting filaments (CFs) is the driving mechanism for the switching effect, it is very important to control the regions where these filaments will evolve. Thus, homolayers of titanium oxide with different oxygen contents were fabricated in order to tune the local electrical and thermal properties of the CFs and narrow down the potential percolation paths. We show that the oxygen content in the top layer of the TiO2-x/TiO2-y bilayer memristors can directly influence the morphology of the layers which affect the diffusion barrier and consequently the diffusivity and drift velocity of oxygen vacancies, yielding in important enhancement of switching characteristics, in terms of spatial uniformity (sigma/mu< 0.2), enlarged switching ratio (similar to 10(4)), and synaptic learning. In order to address the experimental data, a physical model was applied, divulging the crucial role of temperature, electric potential and oxygen vacancy density on the switching effect and offering physical insights to the SET/RESET transitions and the analog switching. The forming free nature of all the devices in conjunction with the self-rectifying behavior, should also be regarded as important assets towards RRAM device optimization. Published by AIP Publishing.