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Abstract

The present paper deals with the stability analysis of a three species ecological model with mutualism, neutralism and prey-predation. Here the second species is a predator preying on the first species and the third species is mutual to the first and neutral to the second species. In addition to the interaction among the species which helps in their respective growth rates, the species are provided with an alternate food resource. Also a more symmetric form of time delay is assumed in the interaction between the predator and the prey species. The model is governed by a system of integro-differential equations. Using Routh-Hurwitz criterion the local stability is established at the interior equilibrium point and a Lyapunov function is constructed to study the global asymptotic stability of the system. Some valid conclusions regarding the sustainability of the system are made at the end using numerical simulation.