Role of time delay and harvesting in some predator–prey communities with different functional responses and intra-species competition

Abstract

ABSTRACT We propose four predator–prey models: RM (Rosenzweig–MacArthur) model, BD model (RM type model with Beddington–DeAngelis functional response), RMI model (i.e., RM model with intraspecific competition among predators) and BDI model (BD model with intraspecific competition among predators). Each model incorporates time delay in the predators’ numerical response. We first analyse the delay-induced stability for all the models. We show that increasing delay always destabilizes a coexisting stable equilibrium in RM and BD models. However, increasing delay does not always destabilize a stable equilibrium in RMI and BDI models. Indeed, the stable equilibrium, in the latter two models, may also maintain its stability due to varying delay. Thus, one of the major conclusions is that the invariance property of the local stability in RMI and BDI models is due to the influence of intraspecific competition. Analytically, we prove that stability switching is impossible to occur in all the models. Later, we implement harvesting of the prey and predator separately, which may generate stability switching. If populations oscillate in the unharvested system, extensive effort has a potential to stabilize the equilibrium. Under the same natural condition (unharvested situation), prey harvesting and predator harvesting may produce opposite dynamic modes.