Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response

Teekam Singh; Ramu Dubey; Vishnu Narayan Mishra; Teekam Singh; Ramu Dubey; Vishnu Narayan Mishra

doi:10.3934/math.2020045

AIMS Mathematics

2020, Volume 5, Issue 1: 673-684. doi: 10.3934/math.2020045

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Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response

1.
School of Allied Sciences, Department of Mathematics, Graphic Era (deemed to be) University, Dehradun, Uttarakhand, PO 248 002, India
2.
Department of Mathematics, Graphic Era Hill University, Dehradun, Uttarakhand, PO 248 002, India
3.
Department of Mathematics, J C Bose University of Science and Technology, YMCA, Faridabad, Haryana, PO 121 006, India
4.
Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak, Madhya Pradesh, PO 484 887, India

Received: 05 September 2019 Accepted: 06 December 2019 Published: 18 December 2019
MSC : 97M10, 93A30, 70K50

In this paper, we have investigated a spatial predator-prey system with hunting cooperation in predators and type-I functional response. Using linear stability analysis, we obtain the stipulations for diffusive instability and identify the corresponding domain in the space of control parameters. Using qualitative and quantitative analysis, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the rate of hunting cooperation in predators and diffusion coefficients of prey and predators. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator-prey model and help us in better understanding of the dynamics of the predator-prey interaction in real environment.
- hunting cooperation,
- spatial patterns,
- diffusive instability,
- reaction-diffusion equations,
- turing bifurcation
Citation: Teekam Singh, Ramu Dubey, Vishnu Narayan Mishra. Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response[J]. AIMS Mathematics, 2020, 5(1): 673-684. doi: 10.3934/math.2020045

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Abstract

In this paper, we have investigated a spatial predator-prey system with hunting cooperation in predators and type-I functional response. Using linear stability analysis, we obtain the stipulations for diffusive instability and identify the corresponding domain in the space of control parameters. Using qualitative and quantitative analysis, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the rate of hunting cooperation in predators and diffusion coefficients of prey and predators. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator-prey model and help us in better understanding of the dynamics of the predator-prey interaction in real environment.

References

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