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 - <p style="text-align: justify;">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.</p>