{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T03:10:25Z","timestamp":1778037025299,"version":"3.51.4"},"reference-count":39,"publisher":"World Scientific Pub Co Pte Ltd","issue":"16","funder":[{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"publisher","award":["20180101221JC"],"award-info":[{"award-number":["20180101221JC"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["20lgpy149"],"award-info":[{"award-number":["20lgpy149"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,12,30]]},"abstract":"<jats:p> This paper investigates the dynamics and optimal control of the Monod\u2013Haldane predator\u2013prey system with mixed harvesting that combines both continuous and impulsive harvestings. The periodic solution of the prey-free is studied and the local stability condition is obtained. The boundedness of solutions, the permanence of the system, and the existence of nontrivial periodic solution are studied. With the change of parameters, the system appears with a stable nontrivial periodic solution when the prey-free periodic solution loses stability. Numerical simulations show that the system has complex dynamical behaviors via bifurcation diagrams. Further, the maximum yield problem of the harvested system is studied, which is transformed into a nonlinear programming problem and solved by the method of combined multiple shooting and collocation. <\/jats:p>","DOI":"10.1142\/s0218127420502430","type":"journal-article","created":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T09:16:23Z","timestamp":1609319783000},"page":"2050243","source":"Crossref","is-referenced-by-count":7,"title":["Dynamics and Optimal Control of a Monod\u2013Haldane Predator\u2013Prey System with Mixed Harvesting"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3924-7783","authenticated-orcid":false,"given":"Xinxin","family":"Liu","sequence":"first","affiliation":[{"name":"Oujiang College, Wenzhou University, Wenzhou 325035, P. R. China"},{"name":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5879-2720","authenticated-orcid":false,"given":"Qingdao","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130012, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,12,28]]},"reference":[{"key":"S0218127420502430BIB001","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1002\/bit.260100602","volume":"10","author":"Andrews J. F.","year":"1968","journal-title":"Biotechnol. Bioeng."},{"key":"S0218127420502430BIB002","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1016\/j.nonrwa.2009.02.021","volume":"11","author":"Baek H. K.","year":"2010","journal-title":"Nonlin. Anal.: Real World Appl."},{"key":"S0218127420502430BIB003","doi-asserted-by":"crossref","first-page":"245","DOI":"10.11650\/twjm\/1500407626","volume":"8","author":"Bai L.","year":"2004","journal-title":"Taiwan. J. Math."},{"key":"S0218127420502430BIB004","volume-title":"Impulsive Differential Equations: Periodic Solutions and Applications","author":"Bainov D.","year":"1993"},{"key":"S0218127420502430BIB005","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0304-3800(99)00220-3","volume":"128","author":"Costa M. I. S.","year":"2000","journal-title":"Ecol. Model."},{"key":"S0218127420502430BIB006","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1016\/j.apm.2008.06.008","volume":"33","author":"Das T.","year":"2009","journal-title":"Appl. Math. Model."},{"key":"S0218127420502430BIB007","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/S0092-8240(86)90004-2","volume":"48","author":"Freedman H. I.","year":"1986","journal-title":"Bull. Math. Biol."},{"key":"S0218127420502430BIB008","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1016\/j.mcm.2007.12.006","volume":"48","author":"Georgescu P.","year":"2008","journal-title":"Math. Comput. Model."},{"key":"S0218127420502430BIB009","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ecolmodel.2013.09.013","volume":"272","author":"Ghosh B.","year":"2014","journal-title":"Ecol. Model."},{"key":"S0218127420502430BIB010","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s10144-014-0436-3","volume":"56","author":"Ghosh B.","year":"2014","journal-title":"Popul. Ecol."},{"key":"S0218127420502430BIB011","doi-asserted-by":"crossref","first-page":"2382","DOI":"10.1016\/j.cnsns.2013.10.033","volume":"19","author":"Gupta R. P.","year":"2014","journal-title":"Commun. Nonlin. Sci. Numer. Simul."},{"key":"S0218127420502430BIB012","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s10255-004-0159-x","volume":"20","author":"Huang J.","year":"2004","journal-title":"Acta Math. Appl. Sin.-Engl. Ser."},{"key":"S0218127420502430BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416500346"},{"key":"S0218127420502430BIB014","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.jmaa.2011.12.049","volume":"390","author":"Jiang D.","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"S0218127420502430BIB015","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.jtbi.2012.11.004","volume":"318","author":"Kar T. K.","year":"2013","journal-title":"J. Theor. Biol."},{"key":"S0218127420502430BIB016","first-page":"265","volume":"7","author":"Lakmeche A.","year":"2000","journal-title":"Dyn. Contin. Discr. Impuls. Syst. Ser. A \u2014 Math. Anal."},{"key":"S0218127420502430BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/0906"},{"key":"S0218127420502430BIB018","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.apm.2016.09.029","volume":"42","author":"Li M.","year":"2017","journal-title":"Appl. Math. Model."},{"key":"S0218127420502430BIB019","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.nonrwa.2004.08.001","volume":"6","author":"Liu B.","year":"2005","journal-title":"Nonlin. Anal.: Real World Appl."},{"key":"S0218127420502430BIB020","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.chaos.2006.03.054","volume":"34","author":"Liu Z.","year":"2007","journal-title":"Chaos Solit. Fract."},{"key":"S0218127420502430BIB021","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.biosystems.2018.05.005","volume":"169","author":"Liu X.","year":"2018","journal-title":"Biosystems"},{"key":"S0218127420502430BIB022","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1186\/s13660-019-2260-y","volume":"2019","author":"Liu X.","year":"2019","journal-title":"J. Inequal. Appl."},{"key":"S0218127420502430BIB023","first-page":"1469","volume":"24","author":"Liu S.","year":"2019","journal-title":"Discr. Contin. Dyn. Syst.-Ser. B"},{"key":"S0218127420502430BIB024","doi-asserted-by":"crossref","first-page":"100816","DOI":"10.1016\/j.ecocom.2020.100816","volume":"42","author":"Liu X.","year":"2020","journal-title":"Ecol. Compl."},{"key":"S0218127420502430BIB025","volume-title":"Elements of Physical Biology","author":"Lotka A. J.","year":"1925"},{"key":"S0218127420502430BIB026","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.cam.2013.03.001","volume":"250","author":"Lv Y.","year":"2013","journal-title":"J. Comput. Appl. Math."},{"key":"S0218127420502430BIB027","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.ecolmodel.2007.04.007","volume":"206","author":"Negi K.","year":"2007","journal-title":"Ecol. Model."},{"key":"S0218127420502430BIB028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ecolmodel.2016.02.010","volume":"328","author":"Paul P.","year":"2016","journal-title":"Ecol. Model."},{"key":"S0218127420502430BIB029","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.cnsns.2017.05.013","volume":"54","author":"Paul P.","year":"2018","journal-title":"Commun. Nonlin. Sci. Numer. Simul."},{"key":"S0218127420502430BIB030","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.marpol.2014.04.002","volume":"49","author":"Reithe S.","year":"2014","journal-title":"Mar. Policy"},{"key":"S0218127420502430BIB031","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.marpol.2017.09.029","volume":"87","author":"Rola A. C.","year":"2018","journal-title":"Mar. Policy"},{"key":"S0218127420502430BIB032","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01086134","volume":"34","author":"Samoilenko A. M.","year":"1982","journal-title":"Ukr. Math. J."},{"key":"S0218127420502430BIB033","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419501529"},{"key":"S0218127420502430BIB034","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02071065","volume":"37","author":"Stryk O. V.","year":"1992","journal-title":"Ann. Oper. Res."},{"key":"S0218127420502430BIB035","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1016\/j.jprocont.2010.06.002","volume":"20","author":"Tamimi J.","year":"2010","journal-title":"J. Process Contr."},{"key":"S0218127420502430BIB037","first-page":"31","volume":"2","author":"Volterra V.","year":"1926","journal-title":"Memoria della Reale Accademia Nazionale dei Lincei"},{"key":"S0218127420502430BIB038","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1186\/s13662-018-1499-9","volume":"2018","author":"Wang J.","year":"2018","journal-title":"Adv. Diff. Eqs."},{"key":"S0218127420502430BIB039","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1137\/S0036139903428719","volume":"65","author":"Xiao D.","year":"2006","journal-title":"SIAM J. Appl. Math."},{"key":"S0218127420502430BIB040","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/S1468-1218(02)00084-6","volume":"4","author":"Zhang X.","year":"2003","journal-title":"Nonlin. Anal.: Real World Appl."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127420502430","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T09:17:09Z","timestamp":1609319829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127420502430"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,28]]},"references-count":39,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2020,12,30]]}},"alternative-id":["10.1142\/S0218127420502430"],"URL":"https:\/\/doi.org\/10.1142\/s0218127420502430","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,28]]}}}