Ferroelectric domain walls differ in their electrical conductivity under different electric and elastic boundary conditions, and this performance can be used to design memories. A phase-field model is developed to explore the effect of elastic, temperature, and toroidal electric fields on the electrical conductivity for a prototype domain-wall memory unit embedded in a center-type quadrant topological domain structure. It shows that the toroidal electric field can switch two states of the domain wall with high and low conductivity repeatedly, and the conductivity can be tuned by the temperature, misfit strain, and thickness. This work might provide significant reference and technical guidance for the design and application of ferroelectric-domain-wall memory.