A predator–prey model characterizing negative effect of prey on its predator

摘要

Predator–prey systems of two species are considered, in which the predator consumes the prey and the prey has a harmful effect on the predator. Our aim is to show that the negative effect of the prey may lead to reduction and/or extinction of its predator, and to show that how and when the reduction/extinction happens. The specific system is a simple extension of the Rosenzweig–MacArthur model by introducing a negative interaction term in the predator equation. By phase-portrait analysis and numerical simulations, we demonstrate that interaction outcomes in the system may transition among predation, amensalism, competition, neutralism and commensalism. First, varying initial densities of species population alone can lead to the transition. In addition, critical regions of the initial densities are exhibited, in which small fluctuation of the densities results in both transition of outcomes and extinction of the predator. Second, varying one or more parameters (factors) may also lead to the transition. Moreover, specific regions of parameters are exhibited, in which small variation of the parameters leads to reduction and/or extinction of the predator.