The accumulation and extrusion of Ca2+ ions in the pre- and post-synaptic terminals play crucial roles in initiating short- and long-term plasticity (STP and LTP) in biological synapses, respectively. Mimicking these synaptic behaviors by electronic devices represents a vital step toward realization of neuromorphic computing. However, the majority of reported synaptic devices usually focus on the emulation of qualitatively synaptic behaviors; devices that can truly emulate the physical behavior of the synaptic Ca2+ ion dynamics in STP and LTP are rarely reported. In this work, Ag/Ag:Ta2O5/Pt self-doping memristors were developed to equivalently emulate the Ca2+ ion dynamics of biological synapses. With conductive filaments from double sources, these memristors produced unique double-switching behavior under voltage sweeps and demonstrated several essential synaptic behaviors under pulse stimuli, including STP, LTP, STP to LTP transition, and spike-rate-dependent plasticity. Experimental results and nanoparticle dynamic simulations both showed that Ag atoms from double sources could mimic Ca2+ dynamics in the pre- and post-synaptic terminals under stimuli. A perceptron network with an STP to LTP transition layer based on the self-doping memristors was also introduced and evaluated; simulations showed that this network could solve noisy figure recognition tasks efficiently. All of these results indicate that the self-doping memristors are promising components for future hardware creation of neuromorphic systems and emulate the characteristics of the brain.