Abstract
In this paper, a class of Nicholson-type delay systems with impulsive effects is considered. First, an equivalence relation between the solution (or positive periodic solution) of a Nicholson-type delay system with impulsive effects and that of the corresponding Nicholson-type delay system without impulsive effects is established. Then, by applying the cone fixed point theorem, some criteria are established for the existence and uniqueness of positive periodic solutions of the given systems. Finally, an example and its simulation are provided to illustrate the main results. Our results extend and improve greatly some earlier works reported in the literature.
Highlights
We consider the following class of Nicholson-type delay systems with impulsive effects:
To describe the population of the Australian sheep-blowfly and to agree with the experimental data obtained in [ ], Gurney et al [ ] proposed the following Nicholson blowflies model:N (t) = –δN(t) + PN(t – τ )e–aN(t–τ), ( . )where N(t) is the size of the population at time t, P is the maximum per capita daily egg production,a is the size at which the population reproduces at its maximum rate, δ is the per capita daily adult death rate, and τ is the generation time
By applying the cone fixed point theorem, some criteria are established for the existence and uniqueness of a positive periodic solution of the given system
Summary
We consider the following class of Nicholson-type delay systems with impulsive effects: We give some criteria ensuring the existence and uniqueness of positive periodic solutions of Nicholson-type delay systems with and without impulses. ≤t≤ω where g is a continuous ω-periodic function defined on R.
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