{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:28:15Z","timestamp":1760146095262,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:00:00Z","timestamp":1727308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Natural Science Foundation","award":["2016GXNSFAA38 0102","42349911"],"award-info":[{"award-number":["2016GXNSFAA38 0102","42349911"]}]},{"name":"National Natural Science Foundation of China","award":["2016GXNSFAA38 0102","42349911"],"award-info":[{"award-number":["2016GXNSFAA38 0102","42349911"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In ecological modeling, symmetry can manifest in multiple ways, significantly contributing to our understanding of ecosystem stability, species interactions, and ecological balance. Considering the bloom phenomenon caused by excessive algae in ponds and its impact on aquaculture, we establish a class of algae\u2013fish ecological models with two state-dependent impulse controls. In this paper, we first discuss the existence of positive equilibria in the system without impulses. Second, the existence and asymptotic stability of the order-1 and order-2 periodic solutions are analyzed by applying successor functions and a Similar Poincare Criterion. Finally, numerical simulations demonstrate that the model exhibits order-1 and order-2 periodic solutions, clarifying that the system with two impulses can address the problem more effectively.<\/jats:p>","DOI":"10.3390\/sym16101265","type":"journal-article","created":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T06:55:52Z","timestamp":1727333752000},"page":"1265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling and Dynamic Analysis of Algae\u2013Fish Model with Two State-Dependent Impulse Controls"],"prefix":"10.3390","volume":"16","author":[{"given":"Ying","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"}]},{"given":"Yuan","family":"Zhuang","sequence":"additional","affiliation":[{"name":"College of Mechanical, Naval Architecture and Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"},{"name":"School of Mechanical Engineering, Guangxi University, Nanning 530004, China"}]},{"given":"Qiong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"},{"name":"School of Science, Beibu Gulf University, Qinzhou 535011, China"}]},{"given":"Lizhuang","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Science, Beibu Gulf University, Qinzhou 535011, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Srirengaraj, V., Einar, R., and Hamed, G. (2024). Use of Algae in Aquaculture: A Review. Fishes, 9.","DOI":"10.3390\/fishes9020063"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"737420","DOI":"10.1016\/j.aquaculture.2021.737420","article-title":"Improvement of fish production and water quality in a recirculating aquaculture pond enhanced with bacteria-microalgae association","volume":"547","author":"Wang","year":"2022","journal-title":"Aquaculture"},{"key":"ref_3","unstructured":"Chen, L. (2017). Mathematical Ecology Model and Research Method, Science Press."},{"key":"ref_4","unstructured":"Tang, S., and Xiao, Y. (2019). Biomathematics, Science Press."},{"key":"ref_5","first-page":"1","article-title":"Pest management and geometric theory of semicontinuous dynamical systems","volume":"12","author":"Chen","year":"2011","journal-title":"Beihua Univ. (Nat. 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Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.mbs.2012.03.011","article-title":"The geometrical analysis of a predator-pery model with two state impulses","volume":"238","author":"Zhao","year":"2012","journal-title":"Math. Biosci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4543976","DOI":"10.1155\/2018\/4543976","article-title":"Modelling and qualitative analysis of water hyacinth ecological system with two state-dependent impulse controls","volume":"2018","author":"Fu","year":"2018","journal-title":"Complexity"},{"key":"ref_11","unstructured":"Zhou, M. (2022). Dynamics Analysis of Competing Systems with State Feedback Control, Xinyang Normal University."},{"key":"ref_12","first-page":"125007","article-title":"State feedback impulsive modeling and dynamic analysis of ecological balance in aquaculture water with nutritional utilization rate","volume":"373","author":"Zhang","year":"2020","journal-title":"Appl. Math. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1265\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:03:35Z","timestamp":1760112215000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1265"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,26]]},"references-count":12,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["sym16101265"],"URL":"https:\/\/doi.org\/10.3390\/sym16101265","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,9,26]]}}}