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Spatial Dynamics of a Diffusive Predator-prey Model with Leslie-Gower Functional Response and Strong Allee Effect
  
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KeyWord:Predator-prey model  Leslie-Gower functional response  Allee effect  Turing bifurcation  Amplitude equations  Pattern formation
Author NameAffiliation
Fengru Wei College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
Cuihua Wang College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
Sanling Yuan College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
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Abstract:
      In this paper, spatial dynamics of a diffusive predator-prey model with Leslie-Gower functional response and strong Allee effect is studied. Firstly, we obtain the critical condition of Hopf bifurcation and Turing bifurcation of the PDE model. Secondly, taking self-diffusion coefficient of the prey as bi- furcation parameter, the amplitude equations are derived by using multi-scale analysis methods. Finally, numerical simulations are carried out to verify our theoretical results. The simulations show that with the decrease of self- diffusion coefficient of the prey, the preys present three pattern structures: spot pattern, mixed pattern, and stripe pattern. We also observe the transi- tion from spot patterns to stripe patterns of the prey by changing the intrinsic growth rate of the predator. Our results reveal that both diffusion and the intrinsic growth rate play important roles in the spatial distribution of species.