Turing patterns and long-time behavior in a three-species food-chain model

Handle URI:
http://hdl.handle.net/10754/563678
Title:
Turing patterns and long-time behavior in a three-species food-chain model
Authors:
Parshad, Rana D.; Kumari, Nitu Krishna; Kasimov, Aslan R.; Ait Abderrahmane, Hamid
Abstract:
We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L2(Ω). We perform linear stability analysis and show that the model exhibits the phenomenon of Turing instability, as well as diffusion induced chaos. Various Turing patterns such as stripe patterns, mesh patterns, spot patterns, labyrinth patterns and weaving patterns are obtained, via numerical simulations in 1d as well as in 2d. The Turing and non-Turing space, in terms of model parameters, is also explored. Finally, we use methods from nonlinear time series analysis to reconstruct a low dimensional chaotic attractor of the model, and estimate its fractal dimension. This provides a lower bound, for the fractal dimension of the attractor, of the spatially explicit model. © 2014 Elsevier Inc.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Mathematical Biosciences
Issue Date:
Aug-2014
DOI:
10.1016/j.mbs.2014.06.007
Type:
Article
ISSN:
00255564
Sponsors:
The present research of N. Kumari is supported by UGC under Raman fellowship, Project No. 5-63/2013(IC) and IIT Mandi under the project No. IITM/SG/NTK/008 and DST under IUATC phase 2, Project No. SR/RCUK-DST/IUATC Phase 2/2012-IITM (G).
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorParshad, Rana D.en
dc.contributor.authorKumari, Nitu Krishnaen
dc.contributor.authorKasimov, Aslan R.en
dc.contributor.authorAit Abderrahmane, Hamiden
dc.date.accessioned2015-08-03T12:06:01Zen
dc.date.available2015-08-03T12:06:01Zen
dc.date.issued2014-08en
dc.identifier.issn00255564en
dc.identifier.doi10.1016/j.mbs.2014.06.007en
dc.identifier.urihttp://hdl.handle.net/10754/563678en
dc.description.abstractWe consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L2(Ω). We perform linear stability analysis and show that the model exhibits the phenomenon of Turing instability, as well as diffusion induced chaos. Various Turing patterns such as stripe patterns, mesh patterns, spot patterns, labyrinth patterns and weaving patterns are obtained, via numerical simulations in 1d as well as in 2d. The Turing and non-Turing space, in terms of model parameters, is also explored. Finally, we use methods from nonlinear time series analysis to reconstruct a low dimensional chaotic attractor of the model, and estimate its fractal dimension. This provides a lower bound, for the fractal dimension of the attractor, of the spatially explicit model. © 2014 Elsevier Inc.en
dc.description.sponsorshipThe present research of N. Kumari is supported by UGC under Raman fellowship, Project No. 5-63/2013(IC) and IIT Mandi under the project No. IITM/SG/NTK/008 and DST under IUATC phase 2, Project No. SR/RCUK-DST/IUATC Phase 2/2012-IITM (G).en
dc.publisherElsevier BVen
dc.subjectDiffusion induced chaosen
dc.subjectGlobal attractoren
dc.subjectNonlinear time series analysisen
dc.subjectThree-species food chainen
dc.subjectTuring instabilityen
dc.titleTuring patterns and long-time behavior in a three-species food-chain modelen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalMathematical Biosciencesen
dc.contributor.institutionDepartment of Mathematics, Clarkson University, Potsdam, NY 13699, United Statesen
dc.contributor.institutionSchool of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh 175001, Indiaen
kaust.authorKasimov, Aslan R.en
kaust.authorAit Abderrahmane, Hamiden
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