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: Journal Publication › Article › peer-review

19 Citations (Scopus)

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-3 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
DOIs	https://doi.org/10.1016/j.physa.2016.05.054
Publication status	Published - 1 Nov 2016
Externally published	Yes

Free Keywords

Intra-species competition
Pattern formation
Turing-Hopf bifurcation
Turing-Hopf-Andronov bifurcation
Turing-Saddle-node
Turing-Transcritical bifurcation

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1016/j.physa.2016.05.054

Cite this

@article{e9e115af07ee485784645a03fd394b84,

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-3 Turing-Takens-Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.",

keywords = "Intra-species competition, Pattern formation, Turing-Hopf bifurcation, Turing-Hopf-Andronov bifurcation, Turing-Saddle-node, Turing-Transcritical bifurcation",

author = "Camara, \{B. I.\} and M. Haque and H. Mokrani",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = nov,

day = "1",

doi = "10.1016/j.physa.2016.05.054",

language = "English",

volume = "461",

pages = "374--383",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Patterns formations in a diffusive ratio-dependent predator-prey model of interacting populations

AU - Camara, B. I.

AU - Haque, M.

AU - Mokrani, H.

PY - 2016/11/1

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-3 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-3 Turing-Takens-Bogdanov bifurcation. The paper concludes with discussions of our results in ecology.

KW - Intra-species competition

KW - Pattern formation

KW - Turing-Hopf bifurcation

KW - Turing-Hopf-Andronov bifurcation

KW - Turing-Saddle-node

KW - Turing-Transcritical bifurcation

UR - https://www.scopus.com/pages/publications/84975090432

U2 - 10.1016/j.physa.2016.05.054

DO - 10.1016/j.physa.2016.05.054

M3 - Article

AN - SCOPUS:84975090432

SN - 0378-4371

VL - 461

SP - 374

EP - 383

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

Abstract

Free Keywords

ASJC Scopus subject areas

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this