Experimental and modeling work of neural activity has described recurrent and attractor dynamic patterns in cerebral microcircuits. However, it is still poorly understood whether similar dynamic principles exist or can be generalizable to the large-scale level. Here, we applied dynamic graph theory-based analyses to evaluate the dynamic streams of whole-brain functional connectivity over time across cognitive states. Dynamic connectivity in local networks is located in attentional areas during tasks and primary sensory areas during rest states, and dynamic connectivity in distributed networks converges in the default mode network (DMN) in both task and rest states. Importantly, we find that distinctive dynamic connectivity patterns are spatially associated with Allen Human Brain Atlas genetic transcription levels of synaptic long-term potentiation and long-term depression-related genes. Our findings support the neurobiological basis of large-scale attractor-like dynamics in the heteromodal cortex within the DMN, irrespective of cognitive state.