Abstract
This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is established
Highlights
Since the end of the 19th century, many biological models have been established to illustrate the evolutionary of species, among them, predator-prey models attracted more and more attention of biologists and mathematicians
This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response
By constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is established
Summary
Since the end of the 19th century, many biological models have been established to illustrate the evolutionary of species, among them, predator-prey models attracted more and more attention of biologists and mathematicians. In 1975, Beddington [1] and DeAngelis [2] proposed the predator-prey system with the Beddington-DeAngelis functional response as follows x. Li and Takeuchi [3] proposed the following model with both Beddington-DeAngelis functional response and density dependent predator ey (1.2). In [4], Qin and Liu studied the dynamic behavior of the following discrete time competitive system x n 1. In [5], Wu and Li considered the following discrete time predator-prey system with hassell-varley type functional response m. We always assume that a n , b n , c n , d n , e n , f n , m1 n , m2 n , m3 n are all positive bounded sequences and. It is to see that the solutions of (1.4) with the initial condition (1.5) are defined and remain positive for all k N
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