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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

Special Issues: 2nd International Conference on Mathematical Modeling, Applied Analysis and Computation (ICMMAAC-19), August 8–10, 2019, JECRC University, Jaipur, India

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.
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Keywords 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. AIMS Mathematics, 2020, 5(1): 673-684. doi: 10.3934/math.2020045


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This article has been cited by

  • 1. Danxia Song, Chao Li, Yongli Song, Stability and cross-diffusion-driven instability in a diffusive predator–prey system with hunting cooperation functional response, Nonlinear Analysis: Real World Applications, 2020, 54, 103106, 10.1016/j.nonrwa.2020.103106

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