Finite Time Blowup in a Realistic Food-Chain Model

Handle URI:
http://hdl.handle.net/10754/550710
Title:
Finite Time Blowup in a Realistic Food-Chain Model
Authors:
Parshad, Rana ( 0000-0001-7443-8927 ) ; Ait Abderrahmane, Hamid; Upadhyay, Ranjit Kumar; Kumari, Nitu ( 0000-0002-2386-785X )
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.
KAUST Department:
Applied Mathematics and Computational Science Program
Citation:
Finite Time Blowup in a Realistic Food-Chain Model 2013, 2013:1 ISRN Biomathematics
Publisher:
Hindawi Publishing Corporation
Journal:
ISRN Biomathematics
Issue Date:
19-May-2013
DOI:
10.1155/2013/424062
Type:
Article
ISSN:
2090-7702
Additional Links:
http://www.hindawi.com/journals/isrn.biomathematics/2013/424062/
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorParshad, Ranaen
dc.contributor.authorAit Abderrahmane, Hamiden
dc.contributor.authorUpadhyay, Ranjit Kumaren
dc.contributor.authorKumari, Nituen
dc.date.accessioned2015-04-27T16:17:38Zen
dc.date.available2015-04-27T16:17:38Zen
dc.date.issued2013-05-19en
dc.identifier.citationFinite Time Blowup in a Realistic Food-Chain Model 2013, 2013:1 ISRN Biomathematicsen
dc.identifier.issn2090-7702en
dc.identifier.doi10.1155/2013/424062en
dc.identifier.urihttp://hdl.handle.net/10754/550710en
dc.description.abstractWe 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.en
dc.publisherHindawi Publishing Corporationen
dc.relation.urlhttp://www.hindawi.com/journals/isrn.biomathematics/2013/424062/en
dc.rightsThis 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.en
dc.titleFinite Time Blowup in a Realistic Food-Chain Modelen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalISRN Biomathematicsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699, USAen
dc.contributor.institutionDepartment of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand 826004, Indiaen
dc.contributor.institutionSchool of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh 175 001, Indiaen
kaust.authorParshad, Ranaen
kaust.authorAit Abderrahmane, Hamiden
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