{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:57:55Z","timestamp":1770836275182,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T00:00:00Z","timestamp":1546905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s12190-018-01232-z","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T04:58:14Z","timestamp":1547009894000},"page":"673-701","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["The impact of provision of additional food to predator in predator\u2013prey model with combined harvesting in the presence of toxicity"],"prefix":"10.1007","volume":"60","author":[{"given":"Reenu","family":"Rani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sunita","family":"Gakkhar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,1,8]]},"reference":[{"key":"1232_CR1","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0022-5193(81)90106-5","volume":"93","author":"TG Hallam","year":"1982","unstructured":"Hallam, T.G., Clark, C.W.: Non-autonomous logistic equations as models of populations in a deteriorating environment. J. Theor. Biol. 93, 303\u2013311 (1982)","journal-title":"J. Theor. Biol."},{"key":"1232_CR2","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF00275908","volume":"18","author":"TG Hallam","year":"1983","unstructured":"Hallam, T.G., Clark, C.E., Jordan, G.S.: Effects of toxicants on populations: a qualitative approach II, first order kinetics. J. Math. Biol. 18, 25\u201337 (1983)","journal-title":"J. Math. Biol."},{"key":"1232_CR3","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/S0022-5193(84)80090-9","volume":"109","author":"TG Hallam","year":"1984","unstructured":"Hallam, T.G., De Luna, T.J.: Effects of toxicants on populations: a qualitative approach III, environmental and food chain pathways. Theor. Biol. 109, 411\u2013429 (1984)","journal-title":"Theor. Biol."},{"key":"1232_CR4","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0304-3800(87)90115-3","volume":"35","author":"J Deluna","year":"1987","unstructured":"Deluna, J., Hallam, T.G.: Effect of toxicants on population: a qualitative approach IV. Resource\u2013consumer\u2013toxicant models. Ecol. Model. 35, 249\u2013273 (1987)","journal-title":"Ecol. Model."},{"key":"1232_CR5","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF00168004","volume":"30","author":"HI Freedman","year":"1990","unstructured":"Freedman, H.I., Shukla, J.B.: Models for the effect of toxicant in a single-species and predator\u2013prey systems. J. Math. Biol. 30, 15\u201330 (1990)","journal-title":"J. Math. Biol."},{"key":"1232_CR6","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0304-3800(00)00228-3","volume":"129","author":"B Dubey","year":"2000","unstructured":"Dubey, B., Hussain, J.: A model for the allelopathic effect on two competing species. Ecol. Model. 129, 195\u2013207 (2000)","journal-title":"Ecol. Model."},{"key":"1232_CR7","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1142\/S0218339001000359","volume":"9","author":"JB Shukla","year":"2001","unstructured":"Shukla, J.B., Agawal, A.K., Dubey, B., Sinha, P.: Existence and survival of two competing species in a polluted environment: a mathematical model. J. Biol. Syst. 9, 89\u2013103 (2001)","journal-title":"J. Biol. Syst."},{"key":"1232_CR8","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.: Effect of toxic substances on a two-species competitive system. Ecol. Model. 84, 287\u2013289 (1996)","journal-title":"Ecol. Model."},{"key":"1232_CR9","volume-title":"Models in Ecology","author":"J Maynard Smith","year":"1974","unstructured":"Maynard Smith, J.: Models in Ecology. Cambridge University Press, Cambridge (1974)"},{"key":"1232_CR10","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/S0304-3800(02)00323-X","volume":"161","author":"TK Kar","year":"2003","unstructured":"Kar, T.K., Chaudhuri, K.S.: On non-selective harvesting of two competing fish species in the presence of toxicity. Ecol. Model. 161, 125\u2013137 (2003)","journal-title":"Ecol. Model."},{"key":"1232_CR11","doi-asserted-by":"publisher","first-page":"2282","DOI":"10.1016\/j.apm.2008.06.008","volume":"33","author":"T Das","year":"2009","unstructured":"Das, T., Mukherjee, R.N., Chaudhuri, K.S.: Harvesting of a prey\u2013predator fishery in the presence of toxicity. Appl. Math. Model. 33, 2282\u20132292 (2009)","journal-title":"Appl. Math. Model."},{"key":"1232_CR12","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1086\/319933","volume":"157","author":"M Baalen van","year":"2001","unstructured":"van Baalen, M., Kivan, V., van Rijn, P.C.J., Sabelis, M.W.: Alternative food, switching predators, and the persistence of predator\u2013prey systems. Am. Nat. 157, 512\u2013524 (2001)","journal-title":"Am. Nat."},{"key":"1232_CR13","doi-asserted-by":"publisher","first-page":"2664","DOI":"10.1890\/0012-9658(2002)083[2664:HPBFPF]2.0.CO;2","volume":"83","author":"PCJ Rijn van","year":"2002","unstructured":"van Rijn, P.C.J., van Houten, Y.M., Abelis, M.W.: How plants benefit from providing food to predators even when it is also edible to herbivores. Ecology 83, 2664\u20132679 (2002)","journal-title":"Ecology"},{"key":"1232_CR14","unstructured":"Harwood, J.D., Obrycki, J.J.: The role of alternative prey in sustaining predator populations. In: Hoddle, M.S. (ed.) Proceedings of the Second International Symposium on the Biological Control of Arthropods, vol. 2, pp. 453\u2013462 (2005)"},{"key":"1232_CR15","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.tpb.2007.03.011","volume":"72","author":"PDN Srinivasu","year":"2007","unstructured":"Srinivasu, P.D.N., Prasad, B.S.R.V., Venkatesulu, M.: Biological control through provision of additional food to predators: a theoretical study. Theor. Popul. Biol. 72, 111\u2013120 (2007)","journal-title":"Theor. Popul. Biol."},{"key":"1232_CR16","doi-asserted-by":"publisher","first-page":"117","DOI":"10.14419\/ijamr.v1i2.38","volume":"1","author":"B Sahoo","year":"2012","unstructured":"Sahoo, B.: Predator\u2013prey model with different growth rates and different functional responses: a comparative study with additional food. Int. J. Appl. Math. Res. 1, 117\u2013129 (2012)","journal-title":"Int. J. Appl. Math. Res."},{"key":"1232_CR17","doi-asserted-by":"publisher","DOI":"10.5402\/2012\/796783","author":"B Sahoo","year":"2012","unstructured":"Sahoo, B.: Effects of additional foods to predators on nutrient consumer predator food chain model. ISRN Biomath. (2012). https:\/\/doi.org\/10.5402\/2012\/796783","journal-title":"ISRN Biomath."},{"key":"1232_CR18","doi-asserted-by":"publisher","first-page":"5653","DOI":"10.1016\/j.apm.2012.11.017","volume":"37","author":"B Sahoo","year":"2013","unstructured":"Sahoo, B., Poria, S.: Disease control in a food chain model supplying alternative food. Appl. Math. Model. 37, 5653\u20135663 (2013)","journal-title":"Appl. Math. Model."},{"key":"1232_CR19","doi-asserted-by":"publisher","first-page":"2249","DOI":"10.1007\/s11538-010-9601-9","volume":"73","author":"PDN Srinivasu","year":"2011","unstructured":"Srinivasu, P.D.N., Prasad, B.S.R.V.: Role of quantity of additional food to predators as a control in predator\u2013prey systems with relevance to pest management and biological conservation. Bull. Math. Biol. 73, 2249\u20132276 (2011)","journal-title":"Bull. Math. Biol."},{"key":"1232_CR20","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1007\/s00285-009-0279-2","volume":"60","author":"PDN Srinivasu","year":"2010","unstructured":"Srinivasu, P.D.N., Prasad, B.S.R.V.: Time optimal control of an additional food provided predator\u2013prey system with applications to pest management and biological conservation. J. Math. Biol. 60, 591\u2013613 (2010)","journal-title":"J. Math. Biol."},{"key":"1232_CR21","first-page":"551","volume":"24","author":"M Nagumo","year":"1942","unstructured":"Nagumo, M.: Uber die Lage der Integralkurven gew onlicher Differentialgleichungen. Proc. Phys. Math. Soc. Jpn. 24, 551 (1942)","journal-title":"Proc. Phys. Math. Soc. Jpn."},{"key":"1232_CR22","series-title":"Texts in Applied Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0249-0","volume-title":"Differential Equations and Dynamical Systems","author":"L Perko","year":"1996","unstructured":"Perko, L.: Differential Equations and Dynamical Systems. Texts in Applied Mathematics, vol. 7, 2nd edn. Springer, New York (1996)","edition":"2"},{"key":"1232_CR23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.amc.2014.10.085","volume":"250","author":"M Sen","year":"2015","unstructured":"Sen, M., Srinivasu, P.D.N., Banerjee, M.: Global dynamics of an additional food provided predator\u2013prey system with constant harvest in predators. Appl. Math. Comput. 250, 193\u2013211 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1232_CR24","volume-title":"Mathematical Bioeconomics: The Optimal Management of Renewable Resources","author":"CW Clark","year":"1976","unstructured":"Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley-Interscience, New York (1976)"},{"key":"1232_CR25","unstructured":"Pontryagin, L.S., Boltyonskii, V.S., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes, Translated from the Russian by K. N. Trirogoff. In: Neustadt, L.W. (ed.) Interscience Publishers, Wiley, New York (1962)"},{"key":"1232_CR26","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1137\/030600746","volume":"27","author":"W Govaerts","year":"2005","unstructured":"Govaerts, W., Kuznetsov, Y.A., Dhooge, A.: Numerical continuation of bifurcations of limit cycles in matlab. SIAM J. Sci. Comput. 27, 231\u2013252 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"1232_CR27","unstructured":"Riet, A.: A Continuation Toolbox in MATLAB. Master thesis, Mathematical Institute, Utrecht University (2000)"},{"key":"1232_CR28","unstructured":"Mestrom, W.: Continuation of Limit Cycles in MATLAB. Master thesis, Mathematical Institute, Utrecht University (2002)"},{"key":"1232_CR29","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1145\/779359.779362","volume":"29","author":"A Dhooge","year":"2003","unstructured":"Dhooge, A., Govaerts, W., Kuznetsov, Y.A.: MATCONT, a Matlab package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29, 141\u2013164 (2003)","journal-title":"ACM Trans. Math. Softw."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-01232-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-018-01232-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-01232-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T23:07:57Z","timestamp":1662764877000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-018-01232-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,8]]},"references-count":29,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["1232"],"URL":"https:\/\/doi.org\/10.1007\/s12190-018-01232-z","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,8]]},"assertion":[{"value":"23 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}