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Qualitative Analysis of a Predator-prey Systemwith Ratio-dependent and Modified Leslie-GowerFunctional Response
  
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KeyWord:Predator-prey model; Modified Leslie-Gower functional response; Stability; Nonconstant positive stationary solution
Author NameAffiliation
Jie Song School of Mathematical Sciences, University of Electronic Science and Tech- nology of China, Chengdu, Sichuan 611731, China 
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Abstract:
      In this paper, a predator-prey model with ratio-dependent and modified Leslie-Gower functional response subject to homogeneous Neumann boundary condition is considered. First, properties of the constant positive sta- tionary solution are shown, including the existence, nonexistence, multiplicity and stability. In addition, a comparatively characterization of the stability is obtained. Moreover, the existing result of global stability is improved. Finally, properties of nonconstant positive stationary solutions are further studied. By a priori estimate and the theory of Leray-Schauder degree, it is shown that nonconstant positive stationary solutions may exist when the system has two constant positive stationary solutions.