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 journalArticlepeer-review

31 Scopus citations


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 languageEnglish (US)
Pages (from-to)83-102
Number of pages20
JournalMathematical Biosciences
Issue number1
StatePublished - 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

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Modeling and Simulation
  • Applied Mathematics
  • Statistics and Probability
  • Immunology and Microbiology(all)
  • Medicine(all)


Dive into the research topics of 'Turing patterns and long-time behavior in a three-species food-chain model'. Together they form a unique fingerprint.

Cite this