Finite Time Blowup in a Realistic Food-Chain Model. (13th June 2013)

• Record Type: Journal Article
• Authors: Parshad, Rana D.; Abderrahmane, Hamid Ait; Upadhyay, Ranjit Kumar; Kumari, Nitu
• Other Names: Pezard L. Academic Editor.; Polezhaev A. A. Academic Editor.
• Is Part Of: ISRN biomathematics. Volume 2013(2013)
• Publication Date: 2013-06-13
• Subjects: Biomathematics -- Periodicals; Models, Biological; Biometry; Biomathematics; Electronic journals; Periodicals; Periodicals; Fulltext; Internet Resources; Periodicals; 570.151
• DOI: 10.1155/2013/424062
• Languages: English
• ISSNs: 2090-7702

Abstract

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.