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

Wei Feng; Nicole Rocco; Michael Freeze; Xin Lu

doi:10.3934/dcdss.2014.7.1215

Article Contents

2014, Volume 7, Issue 6: 1215-1230. Doi: 10.3934/dcdss.2014.7.1215

This issue Previous Article Multiple positive periodic solutions to a predator-prey model with Leslie-Gower Holling-type II functional response and harvesting terms Next Article Duffing-van der Pol-type oscillator systems

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

1.
Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970

Received: January 31, 2013

Revised: July 31, 2013

Published: November 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 34A34, 34C11, 34D23; Secondary: 92D25.

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