@article{Alqahtani2026, 
author = {Nouf Abdulrahman Alqahtani and Mohammadi Begum Jeelani},
title = {A neural network framework for simulating drought impacts on predator– prey dynamics},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {12011-12042},
keywords = {neural networks, predator-prey model, finite difference scheme, drought effects, variable fractional order},
url = {https://www.sciopen.com/article/10.3934/math.2026493},
doi = {10.3934/math.2026493},
abstract = {This study examines the influence of drought on predator–prey systems under the variable-order (VO) fractional derivative. It is applied to the wildebeest–lion system of the Serengeti. First, the well-posedness of the system is ensured by the existence, uniqueness, and Ulam–Hyers (UH) stability of the solution. A finite difference method is presented, coupled with a neural network (NN) approach for numerical validation. The numerical results show the effect of the VO fractional derivative and the intensity of the drought. The results demonstrate that a critical drought threshold exists for the drought impact parameter    γ, beyond which the healthy prey populations decline by over    90  % from 6643 when    γ is 0.20 to 407 when    γ is 0.40, and the risk of extinction is very high. As the fractional order decreases from 0.5, the ecological memory is increased, resulting in increased predator populations (from 4898 to 8974 when    γ is 0.1) and the long-term effects of the drought. The VO framework produces qualitatively different dynamics than constant-order models, featuring time-dependent stability and attractor morphing, which makes it more suitable for modelling real-world ecological systems under climate stress. The NN approach also demonstrates excellent predictive capabilities, achieving        R    2    =  1.0 and RMSE    <  12 for all populations. These metrics validate our numerical scheme and provide a computationally efficient quick scenario analysis. The novelty of our analysis is the combination of a VO operator, finite difference method, and neural computing in a unified framework for analyzing nonlinear fractional ecological systems. This study provides a mathematically sound framework for understanding drought-induced population shifts and offers practical computational tools for ecological forecasting under climate change.}
}