Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response

Xiaozhou Feng, Changtong Li, Hao Sun, Yuzhen Wang, Abdel-Haleem Abdel-Aty
<span title="2021-06-21">2021</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="" style="color: black;">Complexity</a> </i> &nbsp;
In this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey ( λ 1 Ω < a < λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are established by the comparison principle; two local bifurcation solution branches depending on the bifurcation parameter are obtained by local bifurcation theory. Moreover, the demonstrated two local
more &raquo; ... bifurcation solution branches can be extended to a bounded global bifurcation curve by the global bifurcation theory. Second, for the case of the strong growth rate on the prey ( a > λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are obtained by applying reduction to absurdity and the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory. In the end, discussions on the difference of the solution properties between the traditional predator-prey system and the predator-prey system with a spatial degeneracy and B-D functional response are addressed.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1155/2021/9970255</a> <a target="_blank" rel="external noopener" href="">fatcat:44i3v4xvrjgl3ktisztms7xuo4</a> </span>
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