Abstract
A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.
Highlights
In ecology, predator-prey relationship is one of the most important relationship
Chen and Teng [8] discussed the stability of positive equilibrium of a two-species discrete competition system
To investigate the impact of fear effect in discrete predator-prey system, Kundu, Pal, Samanta, et al [31] have discretized the continuous model proposed by Wang, which leads to the following system: r0
Summary
Predator-prey relationship is one of the most important relationship. The interaction between predator and prey is the core of evolutionary biology. In [30], Wang, Zanette and Zou obtained that the fear effect has no influence on the dynamic behaviors of the system with linear functional response Both predator and prey species will go to extinction if r0 < d. To investigate the impact of fear effect in discrete predator-prey system, Kundu, Pal, Samanta, et al [31] have discretized the continuous model proposed by Wang, which leads to the following system: r0. The prey free equilibrium is globally asymptotically stable under some suitable condition This affirms the fact that predators may still be permanent even if the prey populations become extinct, which differs from the result of Wang, Zanette and Zou. To further analyze the complex dynamical behaviors of the discrete system, corresponding to the continuous system (3) we propose the following system:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
