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Mathematical analysis on an extended Rosenzweig-MacArthur model of tri-trophic food chain

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  • In this paper, we study a new model as an extension of the Rosenzweig-MacArthur tritrophic food chain model in which the super-predator consumes both the predator and the prey. We first obtain the ultimate bounds and conditions for exponential convergence for these populations. We also find all possible equilibria and investigate their stability or instability in relation with all the ecological parameters. Our main focus is on the conditions for the existence, uniqueness and stability of a coexistence equilibrium. The complexity of the dynamics in this model is theoretically discussed and graphically demonstrated through various examples and numerical simulations.
    Mathematics Subject Classification: Primary: 34A34, 34C11, 34D23; Secondary: 92D25.


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