- We model the foraging game between a prey and predator when the prey experiences a temporally pulsed resource (e.g., seed-eating gerbils). Animals have the options of foraging or remaining inactive. Prey harvest resources and incur a mortality risk only while foraging. ESS levels of prey and predator activity have three distinct phases over the time course of a resource pulse. During the first phase, resources are sufficiently abundant to permit profitable foraging by all prey and predators. During the second phase, only a fraction of prey and predator are active. The fraction of active prey is sufficient to allow profitable foraging by the predators. Resource abundances and activity level of predators decline synchronously, balancing the prey's needs for food and safety. During the third phase, resources decline to where both prey and predator cease activity. These adaptive behaviors of prey and predator to resources and to each other promote the stability of the predator-prey dynamics.