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Gudermannian neural network procedure for the nonlinear prey-predator dynamical system.

Hafsa Alkaabi¹, Noura Alkarbi¹, Nouf Almemari¹

¹Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box 15551, Al Ain, United Arab Emirates.

|April 11, 2024

Summary

This study introduces Gudermannian neural networks (GNNs) combined with genetic algorithms and interior-point algorithms (GA-IPA) to accurately model nonlinear prey-predator dynamics. The novel GNNs-GA-IPA approach demonstrates high precision and reliability for ecological simulations.

Keywords:

Genetic algorithm Gudermannian neural networks Interior-point algorithm Nonlinear predator-prey system Numerical computing

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Area of Science:

Computational Mathematics
Ecological Modeling
Artificial Intelligence

Background:

Nonlinear dynamics are crucial for understanding complex ecological systems like prey-predator interactions.
Accurate modeling of these systems requires robust numerical methods capable of handling intricate relationships and variable parameters.

Purpose of the Study:

To design and implement a novel Gudermannian neural network (GNN) framework for solving nonlinear dynamics of prey-predator systems (NDPPS).
To integrate global and local search algorithms, specifically genetic algorithm (GA) and interior-point algorithm (IPA), to optimize the GNN model (GNNs-GA-IPA).

Main Methods:

Development of Gudermannian neural networks (GNNs) tailored for NDPPS.
Hybrid optimization strategy combining Genetic Algorithm (GA) and Interior-Point Algorithm (IPA) for GNN training.
Construction and optimization of an error-based merit function using the NDPPS and initial conditions.

Main Results:

The proposed GNNs-GA-IPA effectively solves six cases of NDPPS with variable coefficients.
High accuracy demonstrated by the close agreement between GNNs-GA-IPA results and Runge-Kutta reference solutions.
Achieved absolute errors in the range of 10^-06 to 10^-08, confirming model consistency and reliability.

Conclusions:

The GNNs-GA-IPA hybrid approach provides a highly accurate and reliable method for simulating nonlinear prey-predator dynamics.
Statistical analysis (minimum, median, semi-interquartile ranges) validates the robustness of the model for both predator and prey populations.
The proposed method offers a powerful tool for ecological research and dynamic system analysis.