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A neural network framework for simulating drought impacts on predator- prey dynamics
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DOI：10.3934/math.2026493.png)
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Abstract
En 中文
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 gamma, beyond which the healthy prey populations decline by over 90% from 6643 when gamma is 0.20 to 407 when gamma 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 gamma 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.
Keywords:
predator-prey model
drought effects
variable fractional order
finite difference scheme
neural networks
Journal
A
IF:
1.8
Papers:
474
Citations:
0