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

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.