{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:40:03Z","timestamp":1740148803315,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T00:00:00Z","timestamp":1714780800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T00:00:00Z","timestamp":1714780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871415","12271466"],"award-info":[{"award-number":["11871415","12271466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s12190-024-02095-3","type":"journal-article","created":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T10:01:38Z","timestamp":1714816898000},"page":"3291-3330","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bifurcation analysis of an algal blooms dynamical model in trophic interaction"],"prefix":"10.1007","volume":"70","author":[{"given":"Qian","family":"Wei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liming","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,4]]},"reference":[{"issue":"2","key":"2095_CR1","first-page":"405","volume":"27","author":"IR Belshiasheela","year":"2020","unstructured":"Belshiasheela, I.R., Ghosh, M.: Impact of overfishing of large predatory fish on algal blooms: a mathematical study. Nonlinear Stud. 27(2), 405\u2013413 (2020)","journal-title":"Nonlinear Stud."},{"issue":"2","key":"2095_CR2","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s00285-012-0546-5","volume":"67","author":"L Cai","year":"2013","unstructured":"Cai, L., Chen, G., Xiao, D.: Multiparametric bifurcations of an epidemiological model with strong Allee effect. J. Math. Biol. 67(2), 185\u2013215 (2013)","journal-title":"J. Math. Biol."},{"key":"2095_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639","volume-title":"Normal forms and bifurcations of planar vector fields","author":"SN Chow","year":"1994","unstructured":"Chow, S.N., Li, C., Wang, D.: Normal forms and bifurcations of planar vector fields. Cambridge University Press, Cambridge (1994)"},{"issue":"3","key":"2095_CR4","first-page":"401","volume":"14","author":"K Das","year":"2007","unstructured":"Das, K., Sarkar, A.K.: Effect of algal blooms due to trophic interaction: a qualitative study. Dyn. Cont. Discret. Impulsive Syst. Ser. A 14(3), 401\u2013414 (2007)","journal-title":"Dyn. Cont. Discret. Impulsive Syst. Ser. A"},{"issue":"3","key":"2095_CR5","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1017\/S0143385700004119","volume":"7","author":"F Dumortier","year":"1987","unstructured":"Dumortier, F., Roussarie, R., Sotomayor, J.: Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3. Ergod. Theory Dyn. Syst. 7(3), 375\u2013413 (1987)","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"2095_CR6","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1016\/j.nonrwa.2019.04.003","volume":"50","author":"Y Dai","year":"2019","unstructured":"Dai, Y., Zhao, Y., Sang, B.: Four limit cycles in a predator-prey system of Leslie type with generalized Holling type III functional response. Nonlinear Anal. Real World Appl. 50, 218\u2013239 (2019)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"2095_CR7","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/978-3-319-70069-4_19","volume-title":"Global ecology and oceanography of harmful algal blooms","author":"PJS Franks","year":"2018","unstructured":"Franks, P.J.S.: Recent advances in modelling of harmful algal blooms. In: Glibert, P., Berdalet, E., Burford, M., Pitcher, G., Zhou, M. (eds.) Global ecology and oceanography of harmful algal blooms, pp. 359\u2013377. Springer, Cham (2018)"},{"issue":"4","key":"2095_CR8","doi-asserted-by":"publisher","first-page":"2191","DOI":"10.1016\/j.nonrwa.2009.06.009","volume":"11","author":"NH Gazi","year":"2010","unstructured":"Gazi, N.H., Das, K.: Structural stability analysis of an algal bloom mathematical model in tropic interaction. Nonlinear Anal. Real World Appl. 11(4), 2191\u20132206 (2010)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"2095_CR9","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.hal.2016.05.003","volume":"57","author":"LM Grattan","year":"2016","unstructured":"Grattan, L.M., Holobaugh, S., Morris, J.G.: Harmful algal blooms and public health. Harmful Algae 57, 2\u20138 (2016)","journal-title":"Harmful Algae"},{"issue":"8","key":"2095_CR10","first-page":"2101","volume":"18","author":"J Huang","year":"2013","unstructured":"Huang, J., Gong, Y., Ruan, S.: Bifurcation analysis in a predator-prey model with constant-yield predator harvesting. Discret. Contin. Dyn. Syst. Ser. B 18(8), 2101\u20132121 (2013)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"issue":"3","key":"2095_CR11","doi-asserted-by":"publisher","first-page":"555","DOI":"10.3934\/dcdss.2021151","volume":"15","author":"A Henderson","year":"2022","unstructured":"Henderson, A., Kose, E., Lewis, A., Swanson, E.R.: Mathematical modeling of algal blooms due to swine CAFOs in Eastern North Carolina. Discret. Cont. Dyn. Syst. 15(3), 555\u2013572 (2022)","journal-title":"Discret. Cont. Dyn. Syst."},{"issue":"3","key":"2095_CR12","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s10884-008-9102-9","volume":"20","author":"Y Lamontage","year":"2008","unstructured":"Lamontage, Y., Coutu, C., Rousseau, C.: Bifurcation analysis of a predator-prey system with generalized Holling type III functional response. J. Dyn. Differ. Equ. 20(3), 535\u2013571 (2008)","journal-title":"J. Dyn. Differ. Equ."},{"issue":"4","key":"2095_CR13","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.3934\/dcdsb.2015.20.1107","volume":"20","author":"C Li","year":"2015","unstructured":"Li, C., Li, J., Ma, Z.: Codimension 3 B-T bifurcation in an epidemic model with nonlinear incidence. Discret. Contin. Dyn. Syst. Ser. B 20(4), 1107\u20131116 (2015)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"issue":"3","key":"2095_CR14","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/s12591-017-0383-5","volume":"29","author":"AK Misra","year":"2021","unstructured":"Misra, A.K., Tiwari, P.K., Chandra, P.: Modeling the control of algal bloom in a lake by applying some external efforts with time delay. Differ. Equ. Dyn. Syst. 29(3), 539\u2013568 (2021)","journal-title":"Differ. Equ. Dyn. Syst."},{"key":"2095_CR15","first-page":"403","volume":"25","author":"M Miller","year":"2017","unstructured":"Miller, M., Joshi, H.R.: Modeling harmful algal blooms in the western basin of lake erie and an economic solution. Neural Parallel Sci. Comput. 25, 403\u2013416 (2017)","journal-title":"Neural Parallel Sci. Comput."},{"key":"2095_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0003-8","volume-title":"Differential equations and dynamical systems","author":"L Perko","year":"2001","unstructured":"Perko, L.: Differential equations and dynamical systems, 3rd edn. Springer, New York (2001)","edition":"3"},{"issue":"1","key":"2095_CR17","doi-asserted-by":"publisher","first-page":"119","DOI":"10.3934\/mbe.2019006","volume":"16","author":"D Song","year":"2019","unstructured":"Song, D., Fan, M., Chen, M., Wang, H.: Dynamics of a periodic stoichiometric model with application in predicting and controlling algal bloom in Bohai Sea off China. Math. Biosci. Eng. 16(1), 119\u2013138 (2019)","journal-title":"Math. Biosci. Eng."},{"key":"2095_CR18","first-page":"1","volume":"4","author":"RR Sarkar","year":"2008","unstructured":"Sarkar, R.R., Pal, J., Das, K.P., Chattopadhyay, J.: Control of harmful algal blooms through input of competitive phytoplankton and the effect of environmental variability. J Calcutta Math. Soc. 4, 1\u20138 (2008)","journal-title":"J Calcutta Math. Soc."},{"issue":"3","key":"2095_CR19","doi-asserted-by":"publisher","first-page":"1650043","DOI":"10.1142\/S1793524516500431","volume":"9","author":"NK Thakur","year":"2016","unstructured":"Thakur, N.K., Tiwari, S.K., Upadhyay, R.K.: Harmful algal blooms in fresh and marine water systems: the role of toxin producing phytoplankton. Int. J. Biomath. 9(3), 1650043 (2016)","journal-title":"Int. J. Biomath."},{"issue":"6","key":"2095_CR20","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/0362-546X(91)90064-8","volume":"17","author":"U Timm","year":"1991","unstructured":"Timm, U., Totaro, S., Okubo, A.: Self-and mutual shading effect on competing algal distribution. Nonlinear Anal. Theory Methods Appl. 17(6), 559\u2013576 (1991)","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"issue":"2","key":"2095_CR21","first-page":"417","volume":"8","author":"D Xiao","year":"2007","unstructured":"Xiao, D., Zhang, F.: Multiple bifurcation of a predator-prey system. Discret. Contin. Dyn. Syst. Ser. B 8(2), 417\u2013433 (2007)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"key":"2095_CR22","unstructured":"Zhang, Z., Ding, T., Huang, W., Dong, Z.: Qualitative theory of differential equations. Transl. Math. Monogr., Amer. Math. Soc (1992)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02095-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-024-02095-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02095-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T17:17:57Z","timestamp":1721755077000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-024-02095-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,4]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["2095"],"URL":"https:\/\/doi.org\/10.1007\/s12190-024-02095-3","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2024,5,4]]},"assertion":[{"value":"5 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2024","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 they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}