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Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and post-synaptic spiking is varied in a controlled fashion. However, the plasticity rules inferred from fitting such data are inevitably unstable, in that given constant pre- and post-synaptic activity the synapse will either fully potentiate or depress. This instability can be held in check by adding additional mechanisms, such as homeostasis. Here we consider an alternative scenario in which the plasticity rule itself is stable. When this is the case, net potentiation or depression only occur when pre- and post-synaptic activity vary in time, e.g. when driven by time-varying inputs. We study how the features of such inputs shape the recurrent synaptic connections in models of neuronal circuits. In the case of oscillatory inputs, the resulting structure is strongly affected by the phase relationship between drive to different neurons. In large networks, distributed phases tend to lead to hierarchical clustering. Our results may be of relevance for understanding the effect of sensory-driven inputs, which are by nature time-varying, on synaptic plasticity, and hence on learning and memory.