TY - JOUR
T1 - Turing patterns and long-time behavior in a three-species food-chain model
AU - Parshad, Rana D.
AU - Kumari, Nitu
AU - Kasimov, Aslan R.
AU - Abderrahmane, Hamid Ait
N1 - Funding Information:
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.
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.
KW - Diffusion induced chaos
KW - Global attractor
KW - Nonlinear time series analysis
KW - Three-species food chain
KW - Turing instability
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
AN - SCOPUS:84904427873
SN - 0025-5564
VL - 254
SP - 83
EP - 102
JO - Mathematical Biosciences
JF - Mathematical Biosciences
IS - 1
ER -
