@article{Liu2026, 
author = {Dazhuo Liu and Xuewen Tan},
title = {Memory-based prey-taxis and environmental stress shape spatiotemporal predator-prey dynamics},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17880-17916},
keywords = {predator–prey model, memory-based prey-taxis, environmental stress, spatiotemporal patterns, mathematical modeling ability},
url = {https://www.sciopen.com/article/10.3934/math.2026729},
doi = {10.3934/math.2026729},
abstract = {This paper investigates a diffusive predator–prey system incorporating memory-based prey-taxis, the Allee effect, and environmental stressors. After establishing global well-posedness and existence conditions for equilibria, we use prey-taxis sensitivity and memory delay as parameters to identify Turing and Hopf bifurcation thresholds. Our results show that strong memory-based prey-taxis suppresses diffusion-driven Turing patterns and restores spatial homogeneity. However, this spatial stabilization does not necessarily imply greater delay tolerance: The critical Hopf delay may decrease with taxis sensitivity, revealing a trade-off between taxis-induced spatial stabilization and delay-induced temporal oscillations. Additionally, we analyze environmental stress, revealing a predator release effect where moderate stress disproportionately suppresses predators, which indirectly leads to an increase in the prey's density. We also identify a mode-jumping phenomenon in the critical delay threshold during stress-induced transitions from ordinary differential equation (ODE) to Turing instability. Finally, the numerical simulations provide a two-parameter stability map delineating four dynamic regions: Stable homogeneous states, stationary Turing patterns, spatially nonhomogeneous periodic solutions, and complex spatiotemporal dynamics from interacting instabilities.}
}