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In this paper, we propose a complex neuro-memristive synapse that exhibits the physiological acts of synaptic potentiation and depression of the human-brain. Specifically, the proposed neuromorphic synapse efficiently imitates the synaptic plasticity, especially long-term potentiation (LTP) and depression (LTD), and short-term facilitation (STF) and depression (STD), phenomena of a biological synapse. Similar to biological synapse, the short- or long-term potentiation (STF and LTP) or depression (STD or LTD) of the memristive synapse are distinguished on the basis of time or repetition of input cycles. The proposed synapse is also designed to exhibit the effect of reuptake and neurotransmitters diffusion processes of a bio-synapse. In addition, it exhibits the distinct bio-realistic attributes, i.e., strong stimulation, exponentially decaying conductance trace of synapse, and voltage dependent synaptic responses, of a neuron. The neuro-memristive synapse is designed in SPICE and its bio-realistic functionalities are demonstrated via various simulations. [ABSTRACT FROM AUTHOR]