{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T15:01:48Z","timestamp":1761490908056,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,12,15]]},"abstract":"<jats:p> This paper takes the reaction\u2013diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By means of analyzing the eigenvalue spectrum, we show that the persistent positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via Hopf bifurcation when time delay crosses some critical value. Using normal form and center manifold theory, we investigate the stability of the bifurcating branches of periodic solutions and the direction of the Hopf bifurcation. Numerical simulations are carried out to support our theoretical results. <\/jats:p>","DOI":"10.1142\/s021812741950189x","type":"journal-article","created":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T04:28:25Z","timestamp":1575952105000},"page":"1950189","source":"Crossref","is-referenced-by-count":6,"title":["Oscillations Induced by Quiescent Adult Female in a Reaction\u2013Diffusion Model of Wild Aedes Aegypti Mosquitoes"],"prefix":"10.1142","volume":"29","author":[{"given":"A.","family":"Aghriche","sequence":"first","affiliation":[{"name":"Ibn Zohr University, CST Campus Universitaire Ait Melloul Agadir, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9824-9036","authenticated-orcid":false,"given":"R.","family":"Yafia","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire BP 133, Kenitra, Morocco"}]},{"given":"M. A.","family":"Aziz Alaoui","sequence":"additional","affiliation":[{"name":"Normandie Univ, France"},{"name":"ULH, LMAH, F-76600 Le Havre, France"},{"name":"FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France"}]},{"given":"A.","family":"Tridane","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University Al Ain, Abu Dhabi, UAE"}]},{"given":"F. A.","family":"Rihan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University Al Ain, Abu Dhabi, UAE"}]}],"member":"219","published-online":{"date-parts":[[2019,12,10]]},"reference":[{"key":"S021812741950189XBIB002","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.18576\/amis\/110419","volume":"11","author":"Carmona Toro S. A.","year":"2017","journal-title":"Appl. Math. 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