Predator Prey Scavenger Model using Holling's Functional Response of Type III and Physics-Informed Deep Neural Networks
Aneesh Panchal, Kirti Beniwal, Vivek Kumar
TL;DR
This work extends classical predator–prey models by incorporating a scavenger population that consumes predator carcasses, using Holling's Type III functional response for prey and predator interactions and Type I for scavenger dead-body feeding. A physics-informed neural network (PINN) with Adam optimization is employed to estimate 14 natural parameters from the American forest dataset, followed by BFGS refinement and Jacobian-based stability analysis of the resulting equilibria. The study demonstrates rich dynamical behaviors across reduced and full systems, validates parameter estimation against real data, and confirms the stability of the three-species coexistence state under the learned parameters. The approach provides a data-driven, mechanistically grounded framework for ecological modeling with potential applications in ecosystem management and conservation planning.
Abstract
Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling's functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters.