In the absence of prey, predator population will:
Without prey or another usable food source, predator intake falls to zero while metabolic maintenance, mortality, and emigration continue. In the Lotka–Volterra equation dP/dt = baNP − mP, setting prey density N to zero gives dP/dt = −mP. Predator abundance then declines exponentially at rate m, assuming a closed population and no immigration. Stabilization would require replacement of deaths through feeding-supported reproduction or external subsidy, while increase is impossible under the model because prey conversion supplies the positive growth term. Oscillation also requires reciprocal fee
Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 14