A charge density wave (CDW) ground state is observed in polycrystalline Cu$_2$Se below 125 K, which corresponds to an energy gap of 40.9 meV and an electron-phonon coupling constant of 0.6. Due to the polycrystalline structure, the Peierls transition
process has been expanded to a wide temperature range from 90 to 160 K. The Hall carrier concentration shows a continuous decrease from 2.1$times$10$^{20}$ to 1.6$times$10$^{20}$ cm$^{-3}$ in the temperature range from 160 K to 80 K, while almost unchanged above 160 K and below 90 K. After entering the CDW ground state, a wave-like fluctuation was observed in the I-V curve near 50 K, which exhibits as a periodic negative differential resistivity in an applied electric field due to the current. We also investigated the doping effect of Zn, Ni, and Te on the CDW ground state. Both Zn and Ni doped Cu$_2$Se show a CDW character with increased energy gap and electron-phonon coupling constant, but no notable Peierls transition was observed in Te doped Cu$_2$Se. Similar wave-like I-V curve was also seen in Cu$_{1.98}$Zn$_{0.02}$Se near 40 K. The regular fluctuation in $it{dc}$ I-V curve was not magnetic field sensitive, but temperature and sample size sensitive.
