full
search.png

Search

close.png

Cancel

Volume 1, Issue 3
Mathematical Analysis of a Predator-Prey System with Adaptive Prey Motion

Wendi Wang, Giuseppe Mulone, Juan Zhang & Feng Wang

DOI: 10.4208/csiam-ls.SO-2025-0009

CSIAM Trans. Life Sci., 1 (2025), pp. 489-505.

Published online: 2025-10

Preview Full PDF 5 173

Cited by

google scholar semantic scholar
Export citation
  • Abstract

A mathematical model is proposed that describes the adaptive spatial movement of prey towards higher population density to reduce predation risk. The model admits the increased nonlinearity and the global existence of solutions of the system is established in Sobolev space through analytical estimates. The conditions for the Turing instability from a coexistence steady state are obtained, and sharp conditions for the asymptotical stability of the positive equilibrium in a large region are established with the help of a Lyapunov function. Numerical simulations are presented to support the theoretical results and demonstrate the versatility of spatial models.

  • Keywords

Prey aggregation, group defense, global existence, equilibrium stability, spatial pattern.

  • AMS Subject Headings

92D25, 35K57

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wendi@swu.edu.cn (Wendi Wang)

giuseppe.mulone@unict.it (Giuseppe Mulone)

zhangjuan55@ncepu.edu.cn (Juan Zhang)

wangfeng@seu.edu.cn (Feng Wang)

  • BibTex
  • RIS
  • TXT
@Article{CSIAM-LS-1-489, author = {Wang , WendiMulone , GiuseppeZhang , Juan and Wang , Feng}, title = {Mathematical Analysis of a Predator-Prey System with Adaptive Prey Motion}, journal = {CSIAM Transactions on Life Sciences}, year = {2025}, volume = {1}, number = {3}, pages = {489--505}, abstract = {

A mathematical model is proposed that describes the adaptive spatial movement of prey towards higher population density to reduce predation risk. The model admits the increased nonlinearity and the global existence of solutions of the system is established in Sobolev space through analytical estimates. The conditions for the Turing instability from a coexistence steady state are obtained, and sharp conditions for the asymptotical stability of the positive equilibrium in a large region are established with the help of a Lyapunov function. Numerical simulations are presented to support the theoretical results and demonstrate the versatility of spatial models.

}, issn = {3006-2721}, doi = {https://doi.org/10.4208/csiam-ls.SO-2025-0009}, url = {http://global-sci.org/intro/article_detail/csiam-ls/24512.html} }
TY - JOUR T1 - Mathematical Analysis of a Predator-Prey System with Adaptive Prey Motion AU - Wang , Wendi AU - Mulone , Giuseppe AU - Zhang , Juan AU - Wang , Feng JO - CSIAM Transactions on Life Sciences VL - 3 SP - 489 EP - 505 PY - 2025 DA - 2025/10 SN - 1 DO - http://doi.org/10.4208/csiam-ls.SO-2025-0009 UR - https://global-sci.org/intro/article_detail/csiam-ls/24512.html KW - Prey aggregation, group defense, global existence, equilibrium stability, spatial pattern. AB -

A mathematical model is proposed that describes the adaptive spatial movement of prey towards higher population density to reduce predation risk. The model admits the increased nonlinearity and the global existence of solutions of the system is established in Sobolev space through analytical estimates. The conditions for the Turing instability from a coexistence steady state are obtained, and sharp conditions for the asymptotical stability of the positive equilibrium in a large region are established with the help of a Lyapunov function. Numerical simulations are presented to support the theoretical results and demonstrate the versatility of spatial models.

Wang , WendiMulone , GiuseppeZhang , Juan and Wang , Feng. (2025). Mathematical Analysis of a Predator-Prey System with Adaptive Prey Motion. CSIAM Transactions on Life Sciences. 1 (3). 489-505. doi:10.4208/csiam-ls.SO-2025-0009
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard