Spiking neural P systems (SN P systems) are models of computation inspired by biological spiking neurons. SN P systems have neurons as spike processors, which are placed on the nodes of a directed and static graph (the edges in the graph are the synapses). In this paper, we introduce a variant called SN P systems with scheduled synapses (SSN P systems). SSN P systems are inspired and motivated by the structural dynamism of biological synapses, while incorporating ideas from nonstatic (i.e., dynamic) graphs and networks. In particular, synapses in SSN P systems are available only at specific durations according to their schedules. The SSN P systems model is a response to the problem of introducing durations to synapses of SN P systems. Since SN P systems are in essence static graphs, it is natural to consider them for dynamic graphs also. We introduce local and global schedule types, also taking inspiration from the above-mentioned sources. We prove that SSN P systems are computationally universal as number generators and acceptors for both schedule types, under a normal form (i.e., a simplifying set of restrictions). The introduction of synapse schedules for either schedule type proves useful in programming the system, despite restrictions in the normal form.