Abstract
The ecological dynamics of prey-predator systems have been extensively studied for 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 grossly unchanged among the immigration systems over the classical Previte-Hoffman system.
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