1. A floating memristor, including: a bottom electrode; a top electrode; and a bottom floating gate assembly, formed on the bottom electrode, including a bottom floating gate tunneling layer, a bottom floating gate electrode, and a bottom floating gate barrier layer, from bottom to top; and a nano-battery, formed on a bottom floating gate, composed of a nano-battery anode, a nano-battery electrolyte, and a nano-battery cathode; and a top floating gate assembly, formed on the nano-battery and contacting with the top electrode, including a top floating gate barrier layer, a top floating gate electrode, and a top floating gate tunneling layer from bottom to top; wherein the top electrode, the top floating gate assembly and the nano-battery anode can convert an electric signal to an ion signal by tunneling effect and field effect to simulate a presynaptic membrane; the nano-battery electrolyte is used as an ion channel to simulate a synaptic cleft; the nano-battery cathode, the bottom floating gate, and the bottom-electrode are configured to simulate the postsynaptic membrane, transforming the ion signal into the electronic signal.