Abstract
By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator‐prey system with Hassell‐Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.
Highlights
The dynamic relationship between predators and their prey has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology due to its universal existence and importance 1
The most popular predator-prey model is the one with Holling type II functional response 2 : dx dt ax
1.1 x 0 > 0, y 0 > 0, where x, y denote the density of prey and predator species at time t, respectively
Summary
The dynamic relationship between predators and their prey has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology due to its universal existence and importance 1. A general predator-prey model with Hassell-Varley tape functional response may take the following form: dx dt x a. Cxy myr x, dy dt y −d fx myr x , r ∈ 0, 1 , 1.3 x 0 > 0, y 0 > 0 This model is appropriate for interactions, where predators form groups and have applications in biological control. On the other hand, when the size of the population is rarely small or the population has nonoverlapping generation, the discrete time models are more appropriate than the continuous ones 12–24. This motivated us to propose and study the discrete analogous of predator-prey system 1.3 : xk 1 xk exp ak.
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