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Stationary Pattern of a Reaction–Diffusion Mussel–Algae Model

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Abstract

In this paper, we consider a reaction–diffusion mussel–algae model with state-dependent mussel mortality. This mortality involves a positive feedback term resulting from the reduction of dislodgment and predation and a negative feedback term resulting from the intraspecific competition for mussel. We first study the global stability of the nonnegative uniform steady states and then focus on the existence and nonexistence of nonconstant positive steady states. The global bifurcation of constant positive steady state is also considered. Our results suggest that the regular patterning in mussel beds may be caused by the high mobility of algae or the low diffusion of mussels.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful comments and valuable suggestions which have improved the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Zuolin Shen & Junjie Wei

  2. School of Science, Jimei University, Xiamen, 361021, Fujian, People’s Republic of China

    Junjie Wei

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  1. Zuolin Shen
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  2. Junjie Wei
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Correspondence to Junjie Wei.

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This research is supported by National Natural Science Foundation of China (No. 11771109).

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Shen, Z., Wei, J. Stationary Pattern of a Reaction–Diffusion Mussel–Algae Model. Bull Math Biol 82, 51 (2020). https://doi.org/10.1007/s11538-020-00727-w

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