Dynamics of the Previte-Hoffman food web model with small immigrations

Abstract

AbstractThe ecological dynamics of prey-predator systems are extensively studied over a century. Previte and Hoffman introduced a three species(predator-prey with an omnivore) model in 2013. We demonstrate the asymptotic stability of the Previte and Hoffman modified model adding with small immigration into the prey or predator or omnivore population. A comparison of dynamics is also drawn with immigration and without immigration. It is worth noting that the qualitative dynamics is unchanged among the immigration system over the classical Previte-Hoffman system.