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Stability Analysis of a Diffusive Predator-prey Model with Hunting Cooperation
  
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KeyWord:Predator-prey model; Hunting cooperation; Stability; Turing bifurcation
Author NameAffiliation
Shuhao Wu School of Mathematical Sciences, Tongji University, Shanghai 200092, China 
Yongli Song Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China 
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Abstract:
      In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.