Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

Sajjad Hossain; Md Manarul Haque; M. Humayun Kabir; M. Osman Gani; Sahabuddin Sarwardi

doi:10.1016/j.rico.2021.100059

Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

Sajjad Hossain, Md Manarul Haque, M. Humayun Kabir, M. Osman Gani, Sahabuddin Sarwardi

Research output: Journal Publication › Article › peer-review

6 Citations (Scopus)

Abstract

The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.

Original language	English
Article number	100059
Journal	Results in Control and Optimization
Volume	5
DOIs	https://doi.org/10.1016/j.rico.2021.100059
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

Diffusion
Harvesting
Hopf bifurcation
Numerical simulations
Predator–prey model
Stability
Turing structure

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization
Applied Mathematics
Artificial Intelligence

UN SDGs

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

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10.1016/j.rico.2021.100059

Cite this

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title = "Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function",

abstract = "The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.",

keywords = "Diffusion, Harvesting, Hopf bifurcation, Numerical simulations, Predator–prey model, Stability, Turing structure",

author = "Sajjad Hossain and Haque, {Md Manarul} and Kabir, {M. Humayun} and Gani, {M. Osman} and Sahabuddin Sarwardi",

note = "Publisher Copyright: {\textcopyright} 2021 The Authors",

year = "2021",

month = dec,

doi = "10.1016/j.rico.2021.100059",

language = "English",

volume = "5",

journal = "Results in Control and Optimization",

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T1 - Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

AU - Hossain, Sajjad

AU - Haque, Md Manarul

AU - Kabir, M. Humayun

AU - Gani, M. Osman

AU - Sarwardi, Sahabuddin

PY - 2021/12

Y1 - 2021/12

N2 - The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.

AB - The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.

KW - Diffusion

KW - Harvesting

KW - Hopf bifurcation

KW - Numerical simulations

KW - Predator–prey model

KW - Stability

KW - Turing structure

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U2 - 10.1016/j.rico.2021.100059

DO - 10.1016/j.rico.2021.100059

M3 - Article

AN - SCOPUS:85122753710

SN - 2666-7207

VL - 5

JO - Results in Control and Optimization

JF - Results in Control and Optimization

M1 - 100059

ER -

Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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