2019
DOI: 10.1016/j.jocs.2019.07.002
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Nonstandard finite difference schemes for a general predator–prey system

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 validi… Show more

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Cited by 36 publications
(20 citation statements)
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“…The similar comments can be found in previous works (see, for example, [1, 4, 13-16, 22, 27, 33-36, 40, 41]). The numerical approximations generated by NSFD scheme (10) in Example 3 with t 2 ½0; 100 and h ¼ 2 From Fig. 5, we see that NSFD scheme (10) exactly preserves the essential properties of the continuous model.…”
Section: Numerical Simulationsmentioning
confidence: 92%
See 4 more Smart Citations
“…The similar comments can be found in previous works (see, for example, [1, 4, 13-16, 22, 27, 33-36, 40, 41]). The numerical approximations generated by NSFD scheme (10) in Example 3 with t 2 ½0; 100 and h ¼ 2 From Fig. 5, we see that NSFD scheme (10) exactly preserves the essential properties of the continuous model.…”
Section: Numerical Simulationsmentioning
confidence: 92%
“…(ii) Consider NSFD scheme (10) and suppose that R 0 [ 1. Let /ðhÞ be a function satisfying where the matrix A is given by (16).…”
Section: Theoremmentioning
confidence: 99%
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