Long-term photometric behaviour of the eclipsing Z Cam-type dwarf nova AY Psc

New eclipse timings of the Z Cam-type dwarf nova AY Psc were measured and the orbital ephemeris was revised. Based on the long-term AAVSO data, moreover, the outburst behaviors were also explored. Our analysis suggests that the normal outbursts are quasi-periodic, with an amplitude of $\sim2.5(\pm0.1)$ mag and a period of $\sim18.3(\pm0.7)$ days. The amplitude vs. recurrence-time relation of AY Psc is discussed, and we concluded that this relation may represents general properties of dwarf nova (DN) outbursts. The observed standstill ends with an outburst, which is inconsistent with the general picture of Z Cam-type stars. This unusual behavior was considered to be related to the mass-transfer outbursts. Moreover, the average luminosity is brighter during standstills than during outburst cycles. The changes in brightness marks the variations in $\dot{M}_{2}$ due to the disc of AY Psc is nearly steady state. $\dot{M}_{2}$ value was limited to the range from $6.35\times10^{-9}$ to $1.18\times10^{-8}M_{\odot}yr^{-1}$. More detailed examination shows that there are a few small outbursts presence during standstills. These events with amplitudes of $\sim0.5-0.9$ mag are very similar to the stunted outbursts reported in some NLs. We discussed several possible mechanisms and suggested that the most reasonable mechanism for these stunted outbursts is a changing mass-transfer rate.