Episodic memory has a dynamic nature: when we recall past episodes, we retrieve not only their content, but also their temporal structure. The phenomenon of replay, in the hippocampus of mammals, offers a remarkable example of this temporal dynamics. However, most quantitative models of memory treat memories as static configurations, neglecting the temporal unfolding of the retrieval process. Here, we introduce a continuous attractor network model with a memory-dependent asymmetric component in the synaptic connectivity, which spontaneously breaks the equilibrium of the memory configurations and produces dynamic retrieval. The detailed analysis of the model with analytical calculations and numerical simulations shows that it can robustly retrieve multiple dynamical memories, and that this feature is largely independent of the details of its implementation. By calculating the storage capacity, we show that the dynamic component does not impair memory capacity, and can even enhance it in certain regimes.
