Perception of external stimuli slowly drifts between phases of increased and decreased sensitivity in sustained attention tasks. This phenomenon may represent a deliberate cognitive strategy to balance evidence accumulation against evidence gathering according to the predictive coding hypothesis, or it might simply indicate computational bottlenecks. Here, we claim that dynamical systems theory and large-scale network modeling may offer crucial insights to adjudicate this debate. We attempt to harmonize brain dynamics with dual processing modes by suggesting a link with another aspect of neurotheory: integration and segregation. As a proof of concept, we offer a dynamical systems explanation for recent observations of an anti-correlated relationship between ongoing alpha power and sustained attention, indexed by neural entrainment. Our findings reveal that large-scale coherence within a whole-brain network of alpha oscillators undergoes periodic fluctuations at an ultra-slow rate, leading to a continuous back and forth between integration or segregation biased network states. The in-phase relationship of global and sub-network level coherence oscillations creates dynamical routing states and allows us to postulate a competitive entrainment model of dual attentional modes. Computational and analytic techniques reveal that frustrated synchronization due to modular structural topology, accentuated by heterogeneous cortical oscillatory time scales and conduction delays, is crucial for the emergence of slow periodic modes. We further demonstrate how multiplicative gain instantiated via Cholinergic activity in the presence of conduction delays, may modulate the frequency of slow coherence oscillations, essentially specifying the rate at which sensory cortices parse external stimuli. Our results may have tapped into a general mechanism of ultra-slow fluctuations that abound in neuroscience literature.