Iontronic fluidic ionic/electronic components are emerging as promising elements for artificial brain-like computation systems. Nanopore ionic rectifiers can be operated as a synapse element, exhibiting conductance modulation in response to a train of voltage impulses, thus producing programmable resistive states. We propose a model that replicates hysteresis, rectification, and time domain response properties, based on conductance modulation between two conducting modes and a relaxation time of the state variable. We show that the kinetic effects observed in hysteresis loops govern the potentiation phenomena related to conductivity modulation. To illustrate the efficacy of the model, we apply it to replicate rectification, hysteresis and conductance modulation of two different experimental systems: a polymer membrane with conical pores, and a blind-hole nanoporous anodic alumina membrane with a barrier oxide layer. We show that the time transient analysis of the model develops the observed potentiation and depression phenomena of the synaptic properties.