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We consider a high density of sensors randomly placed in a geographical area for event monitoring. The monitoring regions of the sensors may have significant overlap, and a subset of the sensors can be turned off to conserve energy, thereby increasing the lifetime of the monitoring network. Prior work in this area does not consider the event dynamics. In this paper, we show that knowledge about the event dynamics can be exploited for significant energy savings, by putting the sensors on a periodic on/off schedule. We discuss energy-aware optimization of the periodic schedule for the cases of an synchronous and a asynchronous network. To reduce the overhead of global synchronization, we further consider a spectrum of regionally synchronous networks where the size of the synchronization region is specifiable. Under the periodic scheduling, coordinated sleep by the sensors can be applied orthogonally to minimize the redundancy of coverage and further improve the energy efficiency. We consider the interactions between the periodic scheduling and coordinated sleep. We show that the asynchronous network exceeds any regionally synchronous network in the coverage intensity, thereby increasing the effectiveness of the event capture, though the opportunities for coordinated sleep decreases as the synchronization region gets smaller. When the sensor density is high, the asynchronous network with coordinated sleep can achieve extremely good event capture performance while being highly energy efficient.