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First, for the case of the weak growth rate on the prey (), a priori estimates on any positive steady\u2010state 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 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 priori estimates on any positive steady\u2010state solutions are obtained by applying reduction to absurdity and the set of positive steady\u2010state 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\u2010prey system and the predator\u2010prey system with a spatial degeneracy and B\u2010D functional response are addressed.<\/jats:p>","DOI":"10.1155\/2021\/9970255","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T21:35:11Z","timestamp":1624311311000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Global Bifurcation Structure of a Predator\u2010Prey System with a Spatial Degeneracy and B\u2010D Functional Response"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9349-1432","authenticated-orcid":false,"given":"Xiaozhou","family":"Feng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2979-0005","authenticated-orcid":false,"given":"Changtong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuzhen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_9_1_2","DOI":"10.2307\/3866"},{"doi-asserted-by":"publisher","key":"e_1_2_9_2_2","DOI":"10.2307\/1936298"},{"doi-asserted-by":"publisher","key":"e_1_2_9_3_2","DOI":"10.1186\/s13662-018-1587-x"},{"doi-asserted-by":"publisher","key":"e_1_2_9_4_2","DOI":"10.1016\/j.matcom.2015.05.006"},{"doi-asserted-by":"publisher","key":"e_1_2_9_5_2","DOI":"10.1016\/j.na.2009.09.003"},{"doi-asserted-by":"publisher","key":"e_1_2_9_6_2","DOI":"10.3733\/hilg.v27n14p343"},{"doi-asserted-by":"publisher","key":"e_1_2_9_7_2","DOI":"10.1137\/0517094"},{"key":"e_1_2_9_8_2","first-page":"411","article-title":"Existence and uniqueness of coexistence states for A predator-prey model with diffusion","volume":"7","author":"Casai A.","year":"1994","journal-title":"Differential Integral Equations"},{"doi-asserted-by":"publisher","key":"e_1_2_9_9_2","DOI":"10.1006\/jdeq.1997.3394"},{"doi-asserted-by":"publisher","key":"e_1_2_9_10_2","DOI":"10.1137\/s0036141001387598"},{"doi-asserted-by":"publisher","key":"e_1_2_9_11_2","DOI":"10.1016\/j.egg.2018.05.001"},{"doi-asserted-by":"publisher","key":"e_1_2_9_12_2","DOI":"10.1007\/s40435-018-0407-1"},{"doi-asserted-by":"publisher","key":"e_1_2_9_13_2","DOI":"10.1007\/s40435-018-0490-3"},{"doi-asserted-by":"publisher","key":"e_1_2_9_14_2","DOI":"10.1016\/j.amc.2017.05.040"},{"doi-asserted-by":"publisher","key":"e_1_2_9_15_2","DOI":"10.1007\/s40808-021-01097-5"},{"doi-asserted-by":"publisher","key":"e_1_2_9_16_2","DOI":"10.1016\/j.physa.2019.122301"},{"doi-asserted-by":"publisher","key":"e_1_2_9_17_2","DOI":"10.1088\/1751-8121\/ab81d8"},{"doi-asserted-by":"publisher","key":"e_1_2_9_18_2","DOI":"10.1512\/iumj.2003.52.2196"},{"doi-asserted-by":"publisher","key":"e_1_2_9_19_2","DOI":"10.1137\/s0036141099352844"},{"doi-asserted-by":"publisher","key":"e_1_2_9_20_2","DOI":"10.1016\/0022-1236(71)90015-2"},{"doi-asserted-by":"publisher","key":"e_1_2_9_21_2","DOI":"10.1006\/jdeq.1998.3456"},{"volume-title":"Introduction to Reaction-Diffussion Equations","year":"1990","author":"Ye Q. 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