{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:53Z","timestamp":1740142493710,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T00:00:00Z","timestamp":1619913600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T00:00:00Z","timestamp":1619913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s40314-021-01509-3","type":"journal-article","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T15:46:26Z","timestamp":1620056786000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Mathematical study and optimal control of bioeconomic model concerning harmful dinoflagellate phytoplankton"],"prefix":"10.1007","volume":"40","author":[{"given":"Imane","family":"Agmour","sequence":"first","affiliation":[]},{"given":"Nossaiba","family":"Baba","sequence":"additional","affiliation":[]},{"given":"Meriem","family":"Bentounsi","sequence":"additional","affiliation":[]},{"given":"Naceur","family":"Achtaich","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8207-7057","authenticated-orcid":false,"given":"Youssef","family":"El foutayeni","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,2]]},"reference":[{"issue":"1","key":"1509_CR1","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.jmaa.2010.01.024","volume":"367","author":"S Abbas","year":"2010","unstructured":"Abbas S, Banerjee M, Hungerb\u00fchler N (2010) Existence, uniqueness and stability analysis of allelopathic stimulatory phytoplankton model. J Math Anal Appl 367(1):249\u2013259","journal-title":"J Math Anal Appl"},{"key":"1509_CR2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1155\/2017\/3157294","volume":"3157294","author":"I Agmour","year":"2017","unstructured":"Agmour I, Bentounsi M, El foutayeni Y (2017) Optimization of the two fishermen\u2019s profits exploiting three competing species where prices depend on harvest. Int J Differ Equ 3157294:17. https:\/\/doi.org\/10.1155\/2017\/3157294","journal-title":"Int J Differ Equ"},{"key":"1509_CR3","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.mbs.2018.08.012","volume":"305","author":"I Agmour","year":"2018","unstructured":"Agmour I, Achtaich N, El foutayeni Y (2018) Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco. Math Biosci 305:10\u201317","journal-title":"Math Biosci"},{"issue":"2","key":"1509_CR4","first-page":"108","volume":"26","author":"I Agmour","year":"2018","unstructured":"Agmour I, Achtaich N, El foutayeni Y (2018) Stability analysis of a competing fish populations model with the presence of a predator. Int. J. Nonlinear Sci 26(2):108\u2013121","journal-title":"Int. J. Nonlinear Sci"},{"key":"1509_CR5","doi-asserted-by":"publisher","DOI":"10.28919\/cmbn\/3512","author":"I Agmour","year":"2018","unstructured":"Agmour I, Bentounsi M, Achtaich N, El foutayeni Y (2018) Catchability coefficient influence on the fishermen\u2019s net economic revenues. Commun Math Biol Neurosci. https:\/\/doi.org\/10.28919\/cmbn\/3512","journal-title":"Commun Math Biol Neurosci"},{"key":"1509_CR6","doi-asserted-by":"crossref","unstructured":"Agmour I, Bentounsi M, Baba N, El foutayeni Y, Achtaich N, Aouiti C (2020) Impact of wind speed on fishing effort. Model Earth Syst Environ 6: pp 1-9","DOI":"10.1007\/s40808-020-00736-7"},{"key":"1509_CR7","volume-title":"Public investment, the rate of return, and optimal fiscal policy","author":"KJ Arrow","year":"1970","unstructured":"Arrow KJ, Kurz M (1970) Public investment, the rate of return, and optimal fiscal policy. Johns Hopkins, Baltimore"},{"key":"1509_CR8","unstructured":"Baba N, Agmour I, Achtaich N, El foutayeni Y (2019) The mathematical study for mortality coefficients of small pelagic species. Commun Math Biol Neurosci 2019:1\u201331"},{"issue":"02","key":"1509_CR9","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1142\/S021833900600174X","volume":"14","author":"M Bandyopadhyay","year":"2006","unstructured":"Bandyopadhyay M (2006) Dynamical analysis of a allelopathic phytoplankton model. J Biol Syst 14(02):205\u2013217","journal-title":"J Biol Syst"},{"issue":"3","key":"1509_CR10","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1016\/j.nahs.2008.04.001","volume":"2","author":"M Bandyopadhyay","year":"2008","unstructured":"Bandyopadhyay M, Saha T, Pal R (2008) Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. Nonlinear Anal Hybrid Syst 2(3):958\u2013970","journal-title":"Nonlinear Anal Hybrid Syst"},{"key":"1509_CR11","first-page":"267","volume-title":"Physiological ecology of harmful algal blooms","author":"SS Bates","year":"1998","unstructured":"Bates SS, Garrison DL, Horner RA (1998) Bloom dynamics and physiology of domoic-acid-producing Pseudo-nitzschia species. In: Anderson DM, Cembella AD, Hallegraeff GM (eds) Physiological ecology of harmful algal blooms. Springer-Verlag, Heidelberg, pp 267\u2013292"},{"key":"1509_CR12","doi-asserted-by":"publisher","first-page":"22","DOI":"10.18052\/www.scipress.com\/IFSL.12.22","volume":"12","author":"M Bentounsi","year":"2017","unstructured":"Bentounsi M, Agmour I, Achtaich N, El foutayeni Y (2017) Stability analysis of a biological model of a marine resources allowing density dependent migration. Int Front Sci Lett 12:22\u201334","journal-title":"Int Front Sci Lett"},{"issue":"5","key":"1509_CR13","doi-asserted-by":"publisher","first-page":"5702","DOI":"10.1007\/s40314-018-0658-7","volume":"37","author":"M Bentounsi","year":"2018","unstructured":"Bentounsi M, Agmour I, Achtaich N, El foutayeni Y (2018) The Hopf bifurcation and stability of delayed predator-prey system. Comput Appl Math 37(5):5702\u20135714","journal-title":"Comput Appl Math"},{"key":"1509_CR14","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1155\/2018\/2381483","volume":"10","author":"M Bentounsi","year":"2018","unstructured":"Bentounsi M, Agmour I, Achtaich N, El foutayeni Y (2018) The impact of price on the profits of fishermen exploiting tritrophic prey-predator fish populations. Int J Differ Equ 10:2. https:\/\/doi.org\/10.1155\/2018\/2381483","journal-title":"Int J Differ Equ"},{"issue":"4","key":"1509_CR15","first-page":"362","volume":"9","author":"M Bentounsi","year":"2019","unstructured":"Bentounsi M, Agmour I, Achtaich N, El foutayeni Y (2019) Intrinsic growth rates influence on the net economic rents of fishermen. Int J Dyn Syst Differ Equ 9(4):362\u2013379","journal-title":"Int J Dyn Syst Differ Equ"},{"key":"1509_CR16","volume-title":"Ordinary differential equations","author":"G Birkhoff","year":"1982","unstructured":"Birkhoff G, Rota GC (1982) Ordinary differential equations. Ginn Boston, Boston"},{"key":"1509_CR17","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0304-3800(94)00134-0","volume":"84","author":"J Chattopadhyay","year":"1996","unstructured":"Chattopadhyay J (1996) Effect of toxic substances on a two species competitive system. Ecol Model 84:287\u2013289","journal-title":"Ecol Model"},{"key":"1509_CR18","volume-title":"Mathematical bioeconomics: the optimal management resources","author":"CW Clark","year":"1976","unstructured":"Clark CW (1976) Mathematical bioeconomics: the optimal management resources. Wiley, Hoboken"},{"issue":"3\u20134","key":"1509_CR19","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0304-3800(87)90115-3","volume":"35","author":"JT De Luna","year":"1987","unstructured":"De Luna JT, Hallam TG (1987) Effects of toxicants on populations: a qualitative approach IV. Resource-consumer-toxicant models. Ecol Model 35(3\u20134):249\u2013273","journal-title":"Ecol Model"},{"key":"1509_CR20","first-page":"543","volume":"14","author":"Y El foutayeni","year":"2012","unstructured":"El foutayeni Y (2012) A bio-economic model of fishery where prices depend harvest. J Adv Model Optim 14:543\u2013555","journal-title":"J Adv Model Optim"},{"key":"1509_CR21","first-page":"531","volume":"14","author":"Y El foutayeni","year":"2012","unstructured":"El foutayeni Y, Khaladi M (2012) A generalized bio-economic model for competing multiple-fish populations where prices depend on harvest. J Adv Model Optim 14:531\u2013542","journal-title":"J Adv Model Optim"},{"issue":"1","key":"1509_CR22","first-page":"186","volume":"10","author":"Y El foutayeni","year":"2012","unstructured":"El foutayeni Y, Khaladi M, Zegzouti A (2012) A generalized Nash equilibrium for a bioeconomic problem of fishing. Stud Inf Univ 10(1):186\u2013204","journal-title":"Stud Inf Univ"},{"issue":"2013","key":"1509_CR23","first-page":"457","volume":"15","author":"Y El foutayeni","year":"2013","unstructured":"El foutayeni Y, Khaladi M, Zegzouti A (2013) Profit maximization of fishermen. J Adv Model Optim 15(2013):457\u2013469","journal-title":"J Adv Model Optim"},{"issue":"8","key":"1509_CR24","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1093\/plankt\/15.8.893","volume":"15","author":"KJ Flynn","year":"1993","unstructured":"Flynn KJ, Davidson K (1993) Predator-prey interactions between Isochrysis galbana and Oxyrrhis marina. II. Release of non-protein amines and faeces during predation of Isochrysis. J Plank Res 15(8):893\u2013905","journal-title":"J Plank Res"},{"issue":"1","key":"1509_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF00168004","volume":"30","author":"HI Freedman","year":"1991","unstructured":"Freedman HI, Shukla JB (1991) Models for the effect of toxicant in single-species and predator-prey systems. J Math Biol 30(1):15\u201330","journal-title":"J Math Biol"},{"key":"1509_CR26","doi-asserted-by":"publisher","unstructured":"Hale JK (1971) Functional differential equations. In: Hsieh PF, Stoddart AWJ (eds) Analytic Theory of Differential Equations. Lecture Notes in Mathematics, vol 183. Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/BFb0060406","DOI":"10.1007\/BFb0060406"},{"issue":"2","key":"1509_CR27","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0022-5193(81)90106-5","volume":"93","author":"TG Hallam","year":"1981","unstructured":"Hallam TG, Clark CE (1981) Non-autonomous logistic equations as models of populations in a deteriorating environment. J Theoret Biol 93(2):303\u2013311","journal-title":"J Theoret Biol"},{"issue":"3","key":"1509_CR28","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/S0022-5193(84)80090-9","volume":"109","author":"TG Hallam","year":"1984","unstructured":"Hallam TG, De Luna JT (1984) Effects of toxicants on populations: a qualitative: approach III. Environmental and food chain pathways. J Theoret Biol 109(3):411\u2013429","journal-title":"J Theoret Biol"},{"key":"1509_CR29","first-page":"1","volume":"33","author":"GM Hallegraeff","year":"2003","unstructured":"Hallegraeff GM (2003) Harmful algal blooms: a global overview. Man Harmful Mar Microalgae 33:1\u201322","journal-title":"Man Harmful Mar Microalgae"},{"issue":"1\u20132","key":"1509_CR30","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/S0304-3800(02)00323-X","volume":"161","author":"K Kar","year":"2003","unstructured":"Kar K, Chaudhuri KS (2003) On non-selective harvesting of two competing fish species in the presence of toxicity. Ecol Model 161(1\u20132):125\u2013137","journal-title":"Ecol Model"},{"key":"1509_CR31","first-page":"205","volume":"50","author":"M Kot","year":"2001","unstructured":"Kot M (2001) Elements of mathematical. Ecology 50:205\u2013207","journal-title":"Ecology"},{"key":"1509_CR32","volume-title":"Models in ecology","author":"J Maynard-Smith","year":"1978","unstructured":"Maynard-Smith J (1978) Models in ecology. CUP Archive, Cambridge"},{"issue":"4","key":"1509_CR33","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1093\/plankt\/fbq111","volume":"33","author":"DJ Montagnes","year":"2011","unstructured":"Montagnes DJ, Lowe CD, Martin L, Watts PC, Downes-Tettmar N, Yang Z, Davidson K (2011) Oxyrrhis marina growth, sex and reproduction. J Plankton Res 33(4):615\u2013627","journal-title":"J Plankton Res"},{"issue":"2","key":"1509_CR34","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0025-5564(98)00005-4","volume":"149","author":"A Mukhopadhyay","year":"1998","unstructured":"Mukhopadhyay A, Chattopadhyay J, Tapaswi PK (1998) A delay differential equations model of plankton allelopathy. Math Biosci 149(2):167\u2013189","journal-title":"Math Biosci"},{"issue":"3","key":"1509_CR35","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/S1468-1218(02)00070-6","volume":"4","author":"A Mukhopadhyay","year":"2003","unstructured":"Mukhopadhyay A, Tapaswi PK, Chattopadhyay J (2003) A space-time state-space model of phytoplankton allelopathy. Nonlinear Anal Real World Appl 4(3):437\u2013456","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1509_CR36","doi-asserted-by":"publisher","DOI":"10.1201\/9780203749319","volume-title":"Mathematical theory of optimal processes","author":"LS Pontryagin","year":"2018","unstructured":"Pontryagin LS (2018) Mathematical theory of optimal processes. Routledge, London"},{"key":"1509_CR37","first-page":"560","volume":"24","author":"H Sommer","year":"1937","unstructured":"Sommer H, Meyer KF (1937) Paralytic shell-fish poisoning. Arch Pathol 24:560\u201398","journal-title":"Arch Pathol"},{"key":"1509_CR38","first-page":"537","volume":"24","author":"H Sommer","year":"1937","unstructured":"Sommer H, Whedon WF, Kofoid CA, Stohler R (1937) Relation of paralytic shell-fish poison to certain plankton organisms of the genus Gonyaulax. Arch Pathol 24:537\u201359","journal-title":"Arch Pathol"},{"key":"1509_CR39","first-page":"3","volume-title":"Physiological ecology of harmful algal blooms","author":"FJR Taylor","year":"1998","unstructured":"Taylor FJR (1998) The neurotoxic dinoflagellate genus Alexandrium halim: general introduction. In: Anderson DM, Cembella AD, Hallegraeff GM (eds) Physiological ecology of harmful algal blooms. Springer, Berlin, pp 3\u201311"},{"issue":"11","key":"1509_CR40","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.2331\/suisan.46.1405","volume":"46","author":"T Yasumoto","year":"1980","unstructured":"Yasumoto T, Oshima Y, Sugawara W, Fukuyo Y, Oguri H, Igarashi T, Fujita N (1980) Identification of Dinophysis fortii as the causative organism of diarrhetic shellfish poisoning. Bull Jpn Soc Sci Fish 46(11):1405\u20131411","journal-title":"Bull Jpn Soc Sci Fish"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01509-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01509-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01509-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T20:39:20Z","timestamp":1623098360000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01509-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,2]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1509"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01509-3","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,5,2]]},"assertion":[{"value":"1 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no conflict of interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}],"article-number":"129"}}