Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey
Date of Award
8-2025
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Qingguang Guan
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Huiquing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
This thesis presents a scalable, high-resolution simulation framework for a reaction diffusion prey-predator model with finite hunting ranges. The model’s integral predation term produces stiff, non-local dynamics that present a challenge to traditional explicit or fully implicit solvers. This study overcome this barrier by incorporating a third-order Krylov Subspace Spectral (KSS) time integrator into a Fourier spectral spatial discretization. KSS, which treats each Fourier mode with a frequency-dependent polynomial, avoids the need for solutions of large linear systems in implicit schemes and maintains the computing simplicity of explicit schemes. It also allows for larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations show a variety of spatial and temporal behaviors, including stationary prey refuges, periodic and aperiodic traveling waves, and regime coexistence. These findings support and expand prior analytical predictions for non-local predation.
Copyright
Emmanuel Hackman, 2025
Recommended Citation
Hackman, Emmanuel, "Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey" (2025). Master's Theses. 1145.
https://aquila.usm.edu/masters_theses/1145