ASYMPTOTIC SPREADING FOR A TIME-PERIODIC PREDATOR-PREY SYSTEM

This paper is concerned with asymptotic spreading for a time-periodic predator-prey system where both species synchronously invade a new habitat. Under two different conditions, we show the bounds of spreading speeds of the predator and the prey, which is proved by the theory of asymptotic spreading of scalar equations, comparison principle and generalized eigenvalue. We show either the predator or the prey has a spreading speed that is determined by the linearized equation at the trivial steady state while the spreading speed of the other also depends on the interspecific nonlinearity. From the viewpoint of population dynamics, our results imply that the predator may play a negative effect on the spreading of the prey while the prey may play a positive role on the spreading of the predator.