Global analysis of the ratio-depended predator-prey system with time delay

Ratio-dependent predator-prey models are increasingly favored by field ecologists as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, we consider the global behaviors of solutions of the so-called Michaelis-Menten ratio-dependent predator-prey system with time delay. In addition to confirm that ratio-dependent predator-prey models are rich in boundary dynamics. We also give sufficient conditions for each of the possible steady states to be globally asymptotically stable. We note that for ratio-dependent systems, paradox of enrichment can not occur. In general, local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system, and therefore does not imply global asymptotic stability.