Global stability analysis and persistence for an ecological food web-model

The ecological food web problems and their impact on the environment play vital role for balancing of some environments in our daily life. In the present work, the analytic results of an ecological food web-model are rigorously examined and analyzed. The model includes interactions and natural variables occur in different organisms of the species that influence by the competition and refuge as two basic conditions. The persistence of variant species for the resources competition is also analyzed. The global asymptotic stability of the positive equilibrium points is investigated numerically based on the Runge-Kutta predictor-corrector algorithm. Finally, the effects of the variation of each parameter on the proposed model are inspected numerically.