Abstract
A delayed ratio‐dependent predator‐prey discrete‐time model with nonmonotone functional response is investigated in this paper. By using the continuation theorem of Mawhins coincidence degree theory, some new sufficient conditions are obtained for the existence of multiple positive periodic solutions of the discrete model. An example is given to illustrate the feasibility of the obtained result.
Highlights
It is known that one of important factors impacted on a predator-prey system is the functional response
Ding et al considered a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay 11 ; they obtained some sufficient conditions for the existence and global stability of a positive periodic solution to this system
Based on Mawhins coincidence degree, they obtained some sufficient conditions for the existence of two positive periodic solutions of the ratio-dependent model 1.5
Summary
It is known that one of important factors impacted on a predator-prey system is the functional response. Ding et al considered a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay 11 ; they obtained some sufficient conditions for the existence and global stability of a positive periodic solution to this system. Lu and Wang considered the following discrete semi-ratio-dependent predator-prey system with Holling type IV functional response and time delay 3 : xn 1 xn exp r1 n. They proved that the system 1.6 is permanent and globally attractive under some appropriate conditions. Motivated by the mentioned previously, this paper is to investigate the existence of multiple periodic solutions of the following discrete ratio-dependent model with nonmonotone functional response: exp an. The initial conditions associated with 1.7 are of the form x n φ n , y n ψ n , n∈Z−Z , 1.8 where φ n ≥ 0, ψ n ≥ 0 for n ∈ Z − Z0 and φ 0 > 0, ψ 0 > 0
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