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Firstly, the Poincar\u00e9 map for the phytoplankton-fish model is defined, and the properties of monotonicity, continuity, differentiability, and fixed point of Poincar\u00e9 map are analyzed. In particular, the continuous and discontinuous properties of Poincar\u00e9 map under different conditions are discussed. Secondly, we conduct the analysis of the necessary and sufficient conditions for the existence, uniqueness, and global stability of the order-1 periodic solution of the phytoplankton-fish model and obtain the sufficient conditions for the existence of the order-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math> periodic solution of the system. Numerical simulation shows the correctness of our results which show that phytoplankton and fish with the impulsive feedback control can live stably under certain conditions, and the results have certain reference value for the dynamic change of phytoplankton in aquatic ecosystems.<\/jats:p>","DOI":"10.1155\/2020\/8974763","type":"journal-article","created":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T23:38:33Z","timestamp":1586993913000},"page":"1-13","source":"Crossref","is-referenced-by-count":5,"title":["Dynamic Complexity of a Phytoplankton-Fish Model with the Impulsive Feedback Control by means of Poincar\u00e9 Map"],"prefix":"10.1155","volume":"2020","author":[{"given":"Dezhao","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao, 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