{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:14:27Z","timestamp":1753884867236,"version":"3.41.2"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100015491","name":"Shanghai Institute of Technical Physics, Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["1021GK210006141"],"award-info":[{"award-number":["1021GK210006141"]}],"id":[{"id":"10.13039\/501100015491","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> This work studies a three-dimensional predator\u2013prey model with gestation delay and stage structure between aphidophagous coccinellids and aphid pests, where the interaction between mature coccinellids and aphids is inscribed by Crowley\u2013Martin functional response function, and immature coccinellids and aphids act in the form of Holling-I type. We prove the positivity and boundedness of the solution of the nondelayed system and analyze its equilibrium point, local asymptotic stability, and global stability. In addition to the delays, the critical values of Hopf bifurcation occurring for different parameters are also found from the numerical simulation. The stability of the delayed system and Hopf bifurcation with different delays as parameters are also discussed. Our model analysis shows that the time delay essentially governs the system\u2019s dynamics, and the stability of the system switches as delays increase. We also investigate the direction and stability of the Hopf bifurcation using the normal form theory and center manifold theorem. Finally, we perform computer simulations and depict diagrams to support our theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127423500645","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T09:06:31Z","timestamp":1682672791000},"source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of a Coccinellids-Aphids Model with Stage Structure in Predator Including Maturation and Gestation Delays"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4585-6550","authenticated-orcid":false,"given":"Mengran","family":"Yuan","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Shanghai Institute of Technology, Fengxian District, Shanghai 201418, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8462-2680","authenticated-orcid":false,"given":"Na","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Shanghai Institute of Technology, Fengxian District, Shanghai 201418, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"S0218127423500645BIB001","first-page":"78","volume":"4","author":"Agarwal M.","year":"2012","journal-title":"Int. J. Eng. Sci. Technol."},{"key":"S0218127423500645BIB002","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1046\/j.1570-7458.2003.00021.x","volume":"106","author":"Agarwala B.","year":"2003","journal-title":"Entomol. Exp. 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Simul."},{"key":"S0218127423500645BIB011","volume-title":"Theory and Applications of Hopf Bifurcation","volume":"41","author":"Hassard B. D.","year":"1981"},{"key":"S0218127423500645BIB012","unstructured":"Hodek, I. &  Hon\u00eak, A.  [2013]  Ecology of Coccinellidae, Vol.  54  (Springer Dordrecht Press,  Berlin),  Chapter 8,  pp. 319\u2013350."},{"key":"S0218127423500645BIB013","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.chaos.2015.12.008","volume":"83","author":"Jana D.","year":"2016","journal-title":"Chaos Solit. Fract."},{"key":"S0218127423500645BIB014","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.mcm.2011.08.041","volume":"55","author":"Li F.","year":"2012","journal-title":"Math. Comput. Model."},{"key":"S0218127423500645BIB015","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s12190-013-0674-0","volume":"43","author":"Liu X. Q.","year":"2013","journal-title":"J. Appl. Math. 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