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Volume 16, Issue 1
​Pattern Formation in Rosenzweig–MacArthur Model with Prey–Taxis

Yuanyuan Zhang & Li Xia

Int. J. Numer. Anal. Mod., 16 (2019), pp. 97-115.

Published online: 2018-10

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  • Abstract

In this paper we study the existence and stability of nonconstant positive steady states to a reaction–advection–diffusion system with Rosenzweig–MacArthur kinetics. This system can be used to model the spatial–temporal distributions of predator and prey species . We investigate the effect of prey–taxis on the formation of nonconstant positive steady states in 1D. Stability and instability of these nonconstant steady states are also obtained. We also perform some numerical studies to support the theoretical findings. It is also shown that the Rosenzweig–MacArthur prey–taxis model admits very rich and complicated spatial–temporal dynamics.

  • Keywords

Predator–prey, prey–taxis, steady state, stability analysis.

  • AMS Subject Headings

92C17, 35B32, 35B35, 35B36, 35J47, 35K20, 37K45, 37K50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yyzhang@swufe.edu.cn (Yuanyuan Zhang)

xaleysherry@163.com (Li Xia)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-97, author = {Zhang , Yuanyuan and Xia , Li}, title = {​Pattern Formation in Rosenzweig–MacArthur Model with Prey–Taxis}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {1}, pages = {97--115}, abstract = {

In this paper we study the existence and stability of nonconstant positive steady states to a reaction–advection–diffusion system with Rosenzweig–MacArthur kinetics. This system can be used to model the spatial–temporal distributions of predator and prey species . We investigate the effect of prey–taxis on the formation of nonconstant positive steady states in 1D. Stability and instability of these nonconstant steady states are also obtained. We also perform some numerical studies to support the theoretical findings. It is also shown that the Rosenzweig–MacArthur prey–taxis model admits very rich and complicated spatial–temporal dynamics.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12795.html} }
TY - JOUR T1 - ​Pattern Formation in Rosenzweig–MacArthur Model with Prey–Taxis AU - Zhang , Yuanyuan AU - Xia , Li JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 97 EP - 115 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12795.html KW - Predator–prey, prey–taxis, steady state, stability analysis. AB -

In this paper we study the existence and stability of nonconstant positive steady states to a reaction–advection–diffusion system with Rosenzweig–MacArthur kinetics. This system can be used to model the spatial–temporal distributions of predator and prey species . We investigate the effect of prey–taxis on the formation of nonconstant positive steady states in 1D. Stability and instability of these nonconstant steady states are also obtained. We also perform some numerical studies to support the theoretical findings. It is also shown that the Rosenzweig–MacArthur prey–taxis model admits very rich and complicated spatial–temporal dynamics.

Zhang , Yuanyuan and Xia , Li. (2018). ​Pattern Formation in Rosenzweig–MacArthur Model with Prey–Taxis. International Journal of Numerical Analysis and Modeling. 16 (1). 97-115. doi:
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