Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations

B. I. Camara; M. Haque; H. Mokrani

doi:10.1016/j.physa.2016.05.054

Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations

B. I. Camara
, M. Haque
, H. Mokrani

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

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Abstract

The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator–prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of the present model has been determined.

The emergence of complex patterns in the diffusive predator–prey model is illustrated through numerical simulations. These results are based on the existence of bifurcations of higher codimension such as Turing–Hopf, Turing-Saddle–node, Turing-Transcritical bifurcation, and the codimension- Turing–Takens–Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.

Original language	English
Pages (from-to)	374-383
Number of pages	10
Journal	Physica A: Statistical Mechanics and its Applications
Volume	461
Early online date	8 Jun 2016
DOIs	https://doi.org/10.1016/j.physa.2016.05.054
Publication status	Published - 1 Nov 2016

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Patterns formationsAccepted author manuscript (Post-print), 1.7 MBLicence: CC BY-NC-ND

https://linkinghub.elsevier.com/retrieve/pii/S0378437116302461

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title = "Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations",

abstract = "The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator–prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of the present model has been determined. The emergence of complex patterns in the diffusive predator–prey model is illustrated through numerical simulations. These results are based on the existence of bifurcations of higher codimension such as Turing–Hopf, Turing-Saddle–node, Turing-Transcritical bifurcation, and the codimension- Turing–Takens–Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.",

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AU - Camara, B. I.

AU - Haque, M.

AU - Mokrani, H.

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Y1 - 2016/11/1

N2 - The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator–prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of the present model has been determined. The emergence of complex patterns in the diffusive predator–prey model is illustrated through numerical simulations. These results are based on the existence of bifurcations of higher codimension such as Turing–Hopf, Turing-Saddle–node, Turing-Transcritical bifurcation, and the codimension- Turing–Takens–Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.

AB - The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator–prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of the present model has been determined. The emergence of complex patterns in the diffusive predator–prey model is illustrated through numerical simulations. These results are based on the existence of bifurcations of higher codimension such as Turing–Hopf, Turing-Saddle–node, Turing-Transcritical bifurcation, and the codimension- Turing–Takens–Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations

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