Nonstandard finite difference schemes for a general predator-prey system
Numerical Analysis
2017-01-23 v1
Abstract
In this paper we transform a continuous-time predator-prey system with general functional response and recruitment for both species into a discrete-time model by nonstandard finite difference scheme (NSFD). The NSFD model shows complete dynamic consistency with its continuous counterpart for any step size. Especially, the global stability of a non-hyperbolic equilibrium point in a particular case of parameters is proved by the Lyapunov stability theorem. The performed numerical simulations confirmed the validity of the obtained theoretical results.
Cite
@article{arxiv.1701.05663,
title = {Nonstandard finite difference schemes for a general predator-prey system},
author = {Quang A Dang and Manh Tuan Hoang},
journal= {arXiv preprint arXiv:1701.05663},
year = {2017}
}