{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:41:42Z","timestamp":1774528902850,"version":"3.50.1"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T00:00:00Z","timestamp":1609200000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Youth Fund of China","award":["61102144"],"award-info":[{"award-number":["61102144"]}]},{"name":"National Natural Science Youth Fund of China","award":["2020JM-569"],"award-info":[{"award-number":["2020JM-569"]}]},{"name":"National Natural Science Youth Fund of China","award":["18JK0393"],"award-info":[{"award-number":["18JK0393"]}]},{"name":"National Natural Science Youth Fund of China","award":["2020PSL (Y) 073"],"award-info":[{"award-number":["2020PSL (Y) 073"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["61102144"],"award-info":[{"award-number":["61102144"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["2020JM-569"],"award-info":[{"award-number":["2020JM-569"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["18JK0393"],"award-info":[{"award-number":["18JK0393"]}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["2020PSL (Y) 073"],"award-info":[{"award-number":["2020PSL (Y) 073"]}]},{"DOI":"10.13039\/501100009103","name":"Education Department of Shaanxi Province","doi-asserted-by":"publisher","award":["61102144"],"award-info":[{"award-number":["61102144"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009103","name":"Education Department of Shaanxi Province","doi-asserted-by":"publisher","award":["2020JM-569"],"award-info":[{"award-number":["2020JM-569"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009103","name":"Education Department of Shaanxi Province","doi-asserted-by":"publisher","award":["18JK0393"],"award-info":[{"award-number":["18JK0393"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009103","name":"Education Department of Shaanxi Province","doi-asserted-by":"publisher","award":["2020PSL (Y) 073"],"award-info":[{"award-number":["2020PSL (Y) 073"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Improving Public Scientific Quality in Shaanxi Province","award":["61102144"],"award-info":[{"award-number":["61102144"]}]},{"name":"Project of Improving Public Scientific Quality in Shaanxi Province","award":["2020JM-569"],"award-info":[{"award-number":["2020JM-569"]}]},{"name":"Project of Improving Public Scientific Quality in Shaanxi Province","award":["18JK0393"],"award-info":[{"award-number":["18JK0393"]}]},{"name":"Project of Improving Public Scientific Quality in Shaanxi Province","award":["2020PSL (Y) 073"],"award-info":[{"award-number":["2020PSL (Y) 073"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,12,29]]},"abstract":"<jats:p>This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray\u2013Schauder degree theory and Poincar\u00e9 inequality.<\/jats:p>","DOI":"10.1155\/2020\/8899114","type":"journal-article","created":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T03:35:22Z","timestamp":1609299322000},"page":"1-10","source":"Crossref","is-referenced-by-count":2,"title":["Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9349-1432","authenticated-orcid":true,"given":"Xiaozhou","family":"Feng","sequence":"first","affiliation":[{"name":"College of Science, Xi\u2019an Technological University, Xi\u2019an 710032, China"}]},{"given":"Hao","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Science, Xi\u2019an Technological University, Xi\u2019an 710032, China"}]},{"given":"Yangfan","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Science, Xi\u2019an Technological University, Xi\u2019an 710032, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2895-1727","authenticated-orcid":true,"given":"Feng","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Xi\u2019an Technological University, Xi\u2019an 710032, China"}]}],"member":"311","reference":[{"key":"1","volume-title":"Elements of Physical Biology","author":"A. J. Lotka","year":"1925"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1086\/284409"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.08.020"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-016-0989-1"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1017\/s0308210500031802"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9947-05-04010-9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3969\/j.issn.1005-3085.2019.04.007"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1112\/s0024611503014321"},{"issue":"6","key":"9","first-page":"109","article-title":"A predator-prey system with Beddington-DeAngelis functional response and fear effect","volume":"46","author":"J. Yan","year":"2018","journal-title":"Journal of Southwest University"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-017-0111-8"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1017\/s0308210500000895"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(83)90098-7"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1993.1019"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/7062957"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/3148323"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/9673070"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2006.03.003"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/1950970"},{"issue":"11","key":"19","first-page":"861","article-title":"Existence of coexistent solution and its stability of predator-prey with Monod-Haldane functional response","volume":"34","author":"F. Dai","year":"2014","journal-title":"Journal of Xi\u2019an Technological University"},{"issue":"2","key":"20","first-page":"50","article-title":"Long time behavior of solutions for predator-prey system with saturated competition and Leslie-Gower functional response","volume":"55","author":"Z. Feng","year":"2019","journal-title":"Computer Engineering and Applications"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139901397285"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139999361896"},{"key":"23","volume-title":"Nonlinear Parabolic and Elliptic Equations","author":"C. V. Pao","year":"1992"},{"key":"24","article-title":"Introduction to reaction-diffusion equations","volume-title":"Foundations of Modern Mathematics Series","author":"Q. Ye","year":"2011"},{"key":"25","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0152-3","volume-title":"Shock Waves and Reaction-Diffusion Equations","author":"J. Smoller","year":"1983"},{"key":"26","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1186\/s13662-018-1735-3","article-title":"Permanence, stability, and coexistence of a diffusive predator-prey model with modified Leslie-Gower and BCD functional response","volume":"2018","author":"X. Feng","year":"2018","journal-title":"Advances in Difference Equations"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8899114.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8899114.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8899114.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T03:35:35Z","timestamp":1609299335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/8899114\/"}},"subtitle":[],"editor":[{"given":"Songbai","family":"Guo","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,29]]},"references-count":26,"alternative-id":["8899114","8899114"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8899114","relation":{},"ISSN":["1099-0526","1076-2787"],"issn-type":[{"value":"1099-0526","type":"electronic"},{"value":"1076-2787","type":"print"}],"subject":[],"published":{"date-parts":[[2020,12,29]]}}}