  The X-ray transient XTE J1701-462 was the first source observed to evolve
through all known subclasses of low-magnetic-field neutron star low-mass X-ray
binaries (NS-LMXBs), as a result of large changes in its mass accretion rate.
To investigate to what extent similar evolution is seen in other NS-LMXBs we
have performed a detailed study of the color-color and hardness-intensity
diagrams (CDs and HIDs) of Cyg X-2, Cir X-1, and GX 13+1 -- three luminous
X-ray binaries, containing weakly magnetized neutron stars, known to exhibit
strong secular changes in their CD/HID tracks. Using the full set of Rossi
X-ray Timing Explorer Proportional Counter Array data collected for the sources
over the 16 year duration of the mission, we show that Cyg X-2 and Cir X-1
display CD/HID evolution with close similarities to XTE J1701-462. Although GX
13+1 shows behavior that is in some ways unique, it also exhibits similarities
to XTE J1701-462, and we conclude that its overall CD/HID properties strongly
indicate that it should be classified as a Z source, rather than as an atoll
source. We conjecture that the secular evolution of Cyg X-2, Cir X-1, and GX
13+1 -- illustrated by sequences of CD/HID tracks we construct -- arises from
changes in the mass accretion rate. Our results strengthen previous suggestions
that within single sources Cyg-like Z source behavior takes place at higher
luminosities and mass accretion rates than Sco-like Z behavior, and lend
support to the notion that the mass accretion rate is the primary physical
parameter distinguishing the various NS-LMXB subclasses.
