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Local dynamics of a diffusive predator–prey model in spatially heterogeneous environment

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Abstract

We investigate the effect of dispersal and spatial heterogeneity of the environment on the dynamics of a predator–prey model. In contrast with the homogeneous environment, the dynamics of the model in spatially heterogeneous environment is more complex. For instance, for certain ranges of death and dispersal rates of the predator, the semi-trivial steady state of the model in the heterogeneous case could change its stability multiple times as the dispersal rate of the prey varies from small to large, whereas the stability of the semi-trivial steady state is unaffected by the dispersal rates of the predator and prey in the homogeneous case.

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Acknowledgments

We thank the referee for his helpful comments and suggestions. We thank Dr. Renhao Cui for his help with the figures and Ms. Rui Li for her helpful comments. This research is partially supported by NSFC Grants Nos. 11571364 and 11571363 (YL), NSF Grant DMS-1411476 (YL) and China Scholarship Council (BW). Part of this work was done during the visit of YL to Tokyo Institute of Technology and the visit of BW to Ohio State University. We thank both institutions for the hospitality.

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Authors and Affiliations

  1. Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, People’s Republic of China

    Yuan Lou

  2. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Yuan Lou

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Biao Wang

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  1. Yuan Lou
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  2. Biao Wang
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Correspondence to Yuan Lou.

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Dedicated to Professor Paul Rabinowitz on the occasion of his 77th birthday.

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Lou, Y., Wang, B. Local dynamics of a diffusive predator–prey model in spatially heterogeneous environment. J. Fixed Point Theory Appl. 19, 755–772 (2017). https://doi.org/10.1007/s11784-016-0372-2

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