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Volume 36, Issue 4
A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity

Jiawei Chen & Biao Wang

DOI: 10.4208/jpde.v36.n4.8

J. Part. Diff. Eq., 36 (2023), pp. 435-453.

Published online: 2023-11

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  • Abstract

We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment, where intrinsic growth rate of the prey is spatially homogeneous, whereas carrying capacity of the habitat is spatially inhomogeneous. In comparison with the existing predator-prey models, the stability of semi-trivial steady state of this model displays distinct properties. For example, for certain intermediate ranges of the death rate of the predator, the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large, while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.

  • Keywords

Predator-prey model, carrying capacity, spatial heterogeneity, stability.

  • AMS Subject Headings

35B35, 35K57, 35Q92

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-435, author = {Chen , Jiawei and Wang , Biao}, title = {A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {4}, pages = {435--453}, abstract = {

We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment, where intrinsic growth rate of the prey is spatially homogeneous, whereas carrying capacity of the habitat is spatially inhomogeneous. In comparison with the existing predator-prey models, the stability of semi-trivial steady state of this model displays distinct properties. For example, for certain intermediate ranges of the death rate of the predator, the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large, while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n4.8}, url = {http://global-sci.org/intro/article_detail/jpde/22139.html} }
TY - JOUR T1 - A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity AU - Chen , Jiawei AU - Wang , Biao JO - Journal of Partial Differential Equations VL - 4 SP - 435 EP - 453 PY - 2023 DA - 2023/11 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n4.8 UR - https://global-sci.org/intro/article_detail/jpde/22139.html KW - Predator-prey model, carrying capacity, spatial heterogeneity, stability. AB -

We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment, where intrinsic growth rate of the prey is spatially homogeneous, whereas carrying capacity of the habitat is spatially inhomogeneous. In comparison with the existing predator-prey models, the stability of semi-trivial steady state of this model displays distinct properties. For example, for certain intermediate ranges of the death rate of the predator, the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large, while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.

Jiawei Chen & Biao Wang. (2023). A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity. Journal of Partial Differential Equations. 36 (4). 435-453. doi:10.4208/jpde.v36.n4.8
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