The memristor, the fourth fundamental electric element, was conceptually proposed by L. Chua in 1971 and was found in laboratory late in 2008. Recently a special type of memristor was considered to be able to mimic the behavior of neural synapses. In particular, attributed to the long-term memory of weight changes, the memristor can reproduce the spike-timing-dependent plasticity (STDP) protocol of a synapse, displaying a synaptic modification related to the time interval of pre- and post-synaptic spikes. Not limited to it, we found that the memristor with adaptive thresholds can even mimic higher-order behavior of synapses, realizing the well-known suppression principle of Froemke. This type of memristor can actually express both long-term and short-term plasticities in synapses, which are responsible for the excitation level and the refractory time, respectively. The corresponding dynamical process is governed by a set of ordinary differential equations. Interestingly, the Froemke’s model and our memristor-like model, based on two completely different mechanisms, are found to be quantitatively equivalent. In this chapter we would like to provide this new perspective of looking at synaptic dynamics.
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