Author Summary The study of network fluctuations in time-resolved functional connectivity is a topic of substantial current interest. However, the topic remains hotly disputed, with both positive and negative reports. A number of fundamental issues remain disputed, including statistical benchmarks and putative causes of nonstationarities. Dynamic models of large-scale brain activity can play a key role in this field by proposing the types of instabilities and dynamics that may be present. The purpose of the present paper is to employ simple dynamic models to illustrate the basic processes (“primitives”) that can arise in neuronal ensembles and that might, under the right conditions, cause true nonlinearities and nonstationarities in empirical data. Abstract The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term “dynamic functional connectivity” implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arises under different configurations of local dynamics and intersystem coupling: We show how they generate time series data with nonlinear and/or nonstationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity, and flexibility. The code for simulating these dynamics is available in a freeware software platform, the Brain Dynamics Toolbox.