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

Rana D. Parshad; Nitu Krishna Kumari; Aslan R. Kasimov; Hamid Ait Abderrahmane

doi:10.1016/j.mbs.2014.06.007

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

Rana D. Parshad, Nitu Krishna Kumari, Aslan R. Kasimov, Hamid Ait Abderrahmane

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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.

Original language	English (US)
Pages (from-to)	83-102
Number of pages	20
Journal	Mathematical Biosciences
Volume	254
Issue number	1
DOIs	https://doi.org/10.1016/j.mbs.2014.06.007
State	Published - Aug 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).

ASJC Scopus subject areas

General Agricultural and Biological Sciences
General Biochemistry, Genetics and Molecular Biology
Modeling and Simulation
Applied Mathematics
Statistics and Probability
General Immunology and Microbiology
General Medicine

Access to Document

10.1016/j.mbs.2014.06.007

Cite this

@article{7ef55dcc6f9542648a30c4e68d955f63,

title = "Turing patterns and long-time behavior in a three-species food-chain model",

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. {\textcopyright} 2014 Elsevier Inc.",

author = "Parshad, {Rana D.} and Kumari, {Nitu Krishna} and Kasimov, {Aslan R.} and {Ait Abderrahmane}, Hamid",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).",

year = "2014",

month = aug,

doi = "10.1016/j.mbs.2014.06.007",

language = "English (US)",

volume = "254",

pages = "83--102",

journal = "Mathematical Biosciences",

issn = "0025-5564",

publisher = "Elsevier Inc.",

number = "1",

}

TY - JOUR

T1 - Turing patterns and long-time behavior in a three-species food-chain model

AU - Parshad, Rana D.

AU - Kumari, Nitu Krishna

AU - Kasimov, Aslan R.

AU - Ait Abderrahmane, Hamid

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).

PY - 2014/8

Y1 - 2014/8

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563678

UR - https://linkinghub.elsevier.com/retrieve/pii/S0025556414001138

UR - http://www.scopus.com/inward/record.url?scp=84904427873&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2014.06.007

DO - 10.1016/j.mbs.2014.06.007

M3 - Article

C2 - 24952324

SN - 0025-5564

VL - 254

SP - 83

EP - 102

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 1

ER -

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

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this