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| Investigating the Turing Conditions for Diffusion-driven Instability in Predator-prey System with Hunting Cooperation Functional Response |
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| KeyWord:Reaction-diffusion-ordinary differential equations Steady state solutions Hunting cooperation functional response Carnivorous plants and insects model |
| Author Name | Affiliation | | Shuo Xu | Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China | | Mingzhu Qu | Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China | | Chunrui Zhang | Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China |
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| Abstract: |
| In this paper, we focus on stability analysis of steady-state solutions of a predator-prey system with hunting cooperation functional response. The results show that the Turing instability can be affected not only the existence of hunting cooperation, but also the diffusion coefficients: (1) in the absence of predator diffusion, diffusion-driven instability can be induced by hunting cooperation, but no stable patterns appear; (2) the system can occur diffusion-driven instability and Turing patterns, when both predator and prey have diffusion, and the diffusion coefficient of prey is greater than that of the predator. The numerical simulations of two cases are presented to verify the validity of our theoretical results. |
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