Table of Contents
ISRN Biomathematics
Volume 2013 (2013), Article ID 424062, 12 pages
http://dx.doi.org/10.1155/2013/424062
Research Article

Finite Time Blowup in a Realistic Food-Chain Model

1Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699, USA
2King Abdullah University of Science and Technology, Applied Mathematics and Computational Science, Thuwal 23955-6900, Saudi Arabia
3Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand 826004, India
4School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh 175 001, India

Received 23 April 2013; Accepted 19 May 2013

Academic Editors: L. Pezard and A. A. Polezhaev

Copyright © 2013 Rana D. Parshad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos.