{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:21:50Z","timestamp":1760149310037,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Research Program of Tianshan Talent Plan of Xinjiang, China","award":["2022TSYCJU0005","2023D04045","2021D01C067"],"award-info":[{"award-number":["2022TSYCJU0005","2023D04045","2021D01C067"]}]},{"name":"Open Project of Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region","award":["2022TSYCJU0005","2023D04045","2021D01C067"],"award-info":[{"award-number":["2022TSYCJU0005","2023D04045","2021D01C067"]}]},{"name":"National Natural Science Foundation of Xinjiang","award":["2022TSYCJU0005","2023D04045","2021D01C067"],"award-info":[{"award-number":["2022TSYCJU0005","2023D04045","2021D01C067"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we examine a competitive Nicholson blowflies model with time-varying coefficients and continuous time delays. In the case of coincidence degree theory, constructing appropriate Lyapunov functionals and using several inequalities, several conditions on the extinction, periodic solution, permanence, and global attractiveness of the system are derived. Finally, three examples with numerical simulations are presented to validate the practicability and feasibility of the obtained theoretical results.<\/jats:p>","DOI":"10.3390\/sym15081495","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T01:51:47Z","timestamp":1690509107000},"page":"1495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dynamics in a Competitive Nicholson\u2019s Blowflies Model with Continuous Time Delays"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhiqiao","family":"Wu","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"},{"name":"The Key Laboratory of Applied Mathematics of Xinjiang, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2596-9489","authenticated-orcid":false,"given":"Ahmadjan","family":"Muhammadhaji","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"},{"name":"The Key Laboratory of Applied Mathematics of Xinjiang, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1038\/287017a0","article-title":"Nicholson\u2019s blowflies revisited","volume":"287","author":"Gurney","year":"1980","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/S0895-7177(02)00043-2","article-title":"Oscillation and global attractivity in a periodic Nicholson\u2019s blowflies model","volume":"35","author":"Saker","year":"2002","journal-title":"Math. Comput. Model."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1016\/j.apm.2009.08.027","article-title":"Nicholson\u2019s blowflies differential equations revisited: Main results and open problems","volume":"34","author":"Berezansky","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.nonrwa.2010.06.028","article-title":"Global dynamics of Nicholson-type delay systems with applications","volume":"12","author":"Berezansky","year":"2011","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5581","DOI":"10.1016\/j.apm.2012.10.056","article-title":"The positive periodic solution for Nicholson-type delay system with linear harvesting terms","volume":"37","author":"Zhou","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_6","unstructured":"Jiang, J. (2011). Dynamic Properties of Competitive Nicholson\u2019s Blowflies Model. [Master\u2019s Thesis, Hunan University]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6696453","DOI":"10.1155\/2021\/6696453","article-title":"Dynamics in a nonautonomous Nicholson-type delay system","volume":"2021","author":"Muhammadhaji","year":"2021","journal-title":"J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"012034","DOI":"10.1088\/1742-6596\/2199\/1\/012034","article-title":"Stability analysis of a nontrivial solution for delayed Nicholson blowflies\u2019 model with linear harvesting function","volume":"2199","author":"Ezekiel","year":"2022","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_9","first-page":"1","article-title":"Spreading dynamics of a discrete Nicholson\u2019s blowflies equation with distributed delay","volume":"2023","author":"Wu","year":"2023","journal-title":"Proc. R. Soc. Edinburgh Sect. A Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1007\/s11071-020-05944-5","article-title":"Dynamical behavior of a stochastic Nicholson\u2019s blowflies model with distributed delay and degenerate diffusion","volume":"103","author":"Mu","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106027","DOI":"10.1016\/j.aml.2019.106027","article-title":"New results on stability of Nicholson\u2019s blowflies equation with multiple pairs of time-varying delays","volume":"100","author":"Long","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.3934\/era.2023130","article-title":"Periodic traveling wave solutions of the Nicholson\u2019s blowflies model with delay and advection","volume":"31","author":"Li","year":"2023","journal-title":"Electron. Res. Arch."},{"key":"ref_13","first-page":"14","article-title":"Global asymptotic stability of a scalar delay Nicholson\u2019s blowflies equation in periodic environment","volume":"2022","author":"Ding","year":"2022","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"141","DOI":"10.11650\/tjm\/220803","article-title":"Novel results on persistence and attractivity of delayed Nicholson\u2019s blowflies system with patch structure","volume":"27","author":"Fan","year":"2023","journal-title":"Taiwan. J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2250065","DOI":"10.1142\/S1793524522500656","article-title":"Stochastic Nicholson\u2019s blowflies model with delays","volume":"16","author":"Belmabrouk","year":"2023","journal-title":"Int. J. Biomath."},{"key":"ref_16","first-page":"1091716","article-title":"Dynamic analysis of a model for Spruce Budworm populations with delay","volume":"2021","author":"Muhammadhaji","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Moujahid, A., and Vadillo, F. (2023). Impact of delay on stochastic predator-prey models. Symmetry, 15.","DOI":"10.3390\/sym15061244"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1495\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:21:04Z","timestamp":1760127664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,27]]},"references-count":17,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["sym15081495"],"URL":"https:\/\/doi.org\/10.3390\/sym15081495","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,7,27]]}}}