  Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$
cuprate superconductors. In scanning tunneling microscopy, the detected
charge-order-induced modulation is an electronic response of the charge order.
For an overdoped (Bi,Pb)$_2$Sr$_2$CuO$_{6+x}$ sample, we apply scanning
tunneling microscopy to explore local properties of the charge order. The
ordering wavevector is non-dispersive with energy, which can be confirmed and
determined. By extracting its order-parameter field, we identify dislocations
in the stripe structure of the electronic modulation, which correspond to
topological defects with an integer winding number of $\pm 1$. Through
differential conductance maps over a series of reduced energies, the
development of different response of the charge order is observed and a spatial
evolution of topological defects is detected. The intensity of
charge-order-induced modulation increases with energy and reaches its maximum
when approaching the pseudogap energy. In this evolution, the topological
defects decrease in density and migrate in space. Furthermore, we observe
appearance and disappearance of closely spaced pairs of defects as energy
changes. Our experimental results could inspire further studies of the charge
order in both high-$T_\mathrm{c}$ cuprate superconductors and other charge
density wave materials.
