Multiscale Dynamics of a Tri-Trophic Predator-Prey System with Neural Network Validation

A nonlinear three-species predator-prey model containing populations of prey, intermediate predators, and top predators was proposed and examined. To represent more realistic prey growth and saturation mechanisms inherent in ecological systems, the model incorporates exponential functional responses and restricted prey growth. The model’s qualitative dynamics are examined using equilibrium and local stability analysis, and the population time evolution is numerically examined using the Forward Euler and fourth-order Runge-Kutta (RK4) method. Numerical simulations are used to examine the coexistence behavior, oscillatory dynamics, and asymptotic stability over a long enough period of time. After all, the system tends to a stable coexistence equilibrium since the time-series profiles and phase pictures show that the overall population is positive and bounded under suitable parameter values. The numerical results further demonstrate that the nonlinear trophic interactions between the species cause the species to naturally display transitory oscillations. Furthermore, the results show that the RK4 schemes are more numerically stable than the Euler scheme, especially for larger simulation time steps and smaller error tolerances. Analyzes of parameter sensitivity are also carried out in relation to the intrinsic prey growth rate. The findings demonstrate that, although the species continue to coexist over time, oscillatory behavior is stronger and population fluctuations are larger when the prey growth parameter is higher. The incorporation of restricted prey growth with exponential predator response in a tri-trophic ecological framework and a thorough comparison of traditional numerical techniques for stability and convergence analysis are the innovative aspects of this work. The suggested model advances the mathematical understanding of multispecies population dynamics and provides insightful information on the nonlinear interactions among ecological processes. Furthermore, an artificial neural network (ANN) is used to assess the numerical solutions of the model and learn the numerical adjustment between the RK4 and Euler approximations. The ANN accurately replicates the RK4 time-series and phase-space trajectories, achieving one-step prediction errors of order 10 -7 .