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Spatial Dynamics of a Diffusive Prey-predator Model with Stage Structure and Fear Effect
  
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KeyWord:Prey-predator model; Fear effect; Stage-structured model; Hopf bifurcation; Turing bifurcation; Pattern formation
Author NameAffiliation
Nana Zhu 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:
      To understand the influence of fear effect on population dynamics, especially for the populations with obvious stage structure characteristics, we propose and investigate a diffusive prey-predator model with stage structure in predators. First, we discuss the existence and stability of equilibrium of the model in the absence of diffusion. Then, we obtain the critical conditions for Hopf and Turing bifurcations. Some numerical simulations are also carried out to verify our theoretical results, which indicate that the fear can induce the prey population to show five pattern structures: cold-spot pattern, mixed pattern with cold spots and stripes, stripes pattern, hot-spot pattern, mixed pattern with hot spots and stripes. These findings imply that the fear effect induced by the mature predators plays an important role in the spatial distribution of species.