Abstract
In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.
Highlights
The dynamic relationship between predator and 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]
We study the nonautonomous predator–prey system incorporating prey refuge and Holling type II schemes: x(t) = x(t) a(t) – b(t)x(t) c(t)(x(t) – m(t))y(t)
By applying the comparison theorem of differential equations, a set of conditions that ensure the permanence of the system is obtained
Summary
The dynamic relationship between predator and 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]. We study the nonautonomous predator–prey system incorporating prey refuge and Holling type II schemes: x(t) = x(t) a(t) – b(t)x(t) c(t)(x(t) – m(t))y(t) Proof Let (x(t), y(t))T be any positive solution of the system (1.4) that satisfies the initial condition (1.5). Lemma 2.2 For every positive solution (x(t), y(t))T that satisfies the initial condition (1.5), if the system satisfies (2.1) and al cuM2 al1 – mu dl(m1 – mu) au1 + M1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
