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Dynamics of a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect

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Abstract

In this paper, we consider a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect on prey under homogeneous Neumann boundary condition. Firstly, we investigate the qualitative properties of the system including the persistent property, and local and global asymptotical stability of the unique positive constant equilibrium point of the system. Next, we also show the existence and nonexistence of nonconstant positive steady states of the reaction–diffusion system, which reflect the effect of large diffusivity.

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Acknowledgments

The authors would like to thank the editor and the anonymous referees for their valuable comments and suggestions on this paper. This work was supported by the Program for New Century Excellent Talents in University (NCET-10-0097), the NSFC Tianyuan Foundation (Grant No. 11226256) and the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13A010010).

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  1. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Liu Yang & Shouming Zhong

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  1. Liu Yang
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  2. Shouming Zhong
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Correspondence to Liu Yang.

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Communicated by Antonio José Silva Neto.

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Yang, L., Zhong, S. Dynamics of a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect. Comp. Appl. Math. 34, 671–690 (2015). https://doi.org/10.1007/s40314-014-0131-1

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  • DOI: https://doi.org/10.1007/s40314-014-0131-1

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