{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T19:37:21Z","timestamp":1776973041676,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2014,5,4]],"date-time":"2014-05-04T00:00:00Z","timestamp":1399161600000},"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":["Nonlinear Dyn"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s11071-014-1415-0","type":"journal-article","created":{"date-parts":[[2014,5,3]],"date-time":"2014-05-03T19:55:49Z","timestamp":1399146949000},"page":"1749-1771","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Big bang bifurcations and Allee effect in Blumberg\u2019s dynamics"],"prefix":"10.1007","volume":"77","author":[{"given":"J. Leonel","family":"Rocha","sequence":"first","affiliation":[]},{"given":"Dani\u00e8le","family":"Fournier-Prunaret","sequence":"additional","affiliation":[]},{"given":"Abdel-Kaddous","family":"Taha","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,5,4]]},"reference":[{"key":"1415_CR1","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/0022-5193(68)90058-1","volume":"21","author":"AA Blumberg","year":"1968","unstructured":"Blumberg, A.A.: Logistic growth rate functions. J. Theor. Biol. 21, 42\u201344 (1968)","journal-title":"J. Theor. Biol."},{"issue":"1","key":"1415_CR2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0025-5564(02)00096-2","volume":"179","author":"A Tsoularis","year":"2002","unstructured":"Tsoularis, A., Wallace, J.: Analysis of logistic growth models. Math. Biosci. 179(1), 21\u201355 (2002)","journal-title":"Math. Biosci."},{"key":"1415_CR3","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0025-5564(76)90112-7","volume":"29","author":"ME Turner","year":"1976","unstructured":"Turner, M.E., Bradley, E.L., Kirk, K.A., Pruitt, K.M.: A theory of growth. Math. Biosci. 29, 367\u2013373 (1976)","journal-title":"Math. Biosci."},{"key":"1415_CR4","doi-asserted-by":"crossref","DOI":"10.1515\/9783112621349","volume-title":"The Predator-Prey Model. Do We Leave in a Volterra World?","author":"M Peschel","year":"1986","unstructured":"Peschel, M., Mende, W.: The Predator-Prey Model. Do We Leave in a Volterra World?. Springer, Wien (1986)"},{"key":"1415_CR5","doi-asserted-by":"crossref","unstructured":"Pruitt, K.M., Turner, M.E.: In: Agris, P.F. (ed.) A kinetic theory for analysis of complex systems, in Biomolecular Structure and Function, pp. 257\u2013265. Academic Press, New York (1978)","DOI":"10.1016\/B978-0-12-043950-8.50033-4"},{"key":"1415_CR6","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1080\/716067187","volume":"42","author":"M Carrillo","year":"2002","unstructured":"Carrillo, M., Gonzlez, J.: Fitting a growth model to number of tourist places in Tenerife. Syst. Anal. Model. Simul. 42, 895\u2013906 (2002)","journal-title":"Syst. Anal. Model. Simul."},{"key":"1415_CR7","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.jtbi.2003.11.021","volume":"227","author":"E Skubica","year":"2004","unstructured":"Skubica, E., Taborskya, M., McNamarac, J.M., Houston, A.I.: When to parasitize? A dynamic optimization model of reproductive strategies in a cooperative breeder. J. Theor. Biol. 227, 487\u2013501 (2004)","journal-title":"J. Theor. Biol."},{"key":"1415_CR8","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF00114174","volume":"39","author":"R Buis","year":"1991","unstructured":"Buis, R.: On the generalization of the logistic law of growth. Acta Biotheoretica 39, 185\u2013195 (1991)","journal-title":"Acta Biotheoretica"},{"key":"1415_CR9","volume-title":"Mathematical Bioeconomic: The Optimal Management of Renewable Resources","author":"CW Clark","year":"1990","unstructured":"Clark, C.W.: Mathematical Bioeconomic: The Optimal Management of Renewable Resources. Wiley, New York (1990)"},{"key":"1415_CR10","first-page":"3","volume":"1124","author":"SM Aleixo","year":"2009","unstructured":"Aleixo, S.M., Rocha, J.L., Pestana, D.D.: Populational growth models proportional to beta densities with Allee effect. Am. Inst. Phys. 1124, 3\u201312 (2009)","journal-title":"Am. Inst. Phys."},{"key":"1415_CR11","doi-asserted-by":"crossref","first-page":"201","DOI":"10.2498\/cit.1002098","volume":"20","author":"SM Aleixo","year":"2012","unstructured":"Aleixo, S.M., Rocha, J.L.: Generalized models from $$Beta(p,2)$$ B e t a ( p , 2 ) densities with strong Allee effect: dynamical approach. J. Comput. Inf. Technol. 20, 201\u2013207 (2012)","journal-title":"J. Comput. Inf. Technol."},{"issue":"3","key":"1415_CR12","doi-asserted-by":"crossref","first-page":"783","DOI":"10.3934\/dcdsb.2013.18.783","volume":"18","author":"JL Rocha","year":"2013","unstructured":"Rocha, J.L., Aleixo, S.M.: Dynamical analysis in growth models: Blumberg\u2019s equation. Discret. Contin. Dyn. Syst. Ser. B 18(3), 783\u2013795 (2013)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"key":"1415_CR13","volume-title":"Animal Aggregations","author":"WC Allee","year":"1931","unstructured":"Allee, W.C.: Animal Aggregations. University of Chicago Press, Chicago (1931)"},{"issue":"9","key":"1415_CR14","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.3934\/dcdsb.2013.18.2397","volume":"18","author":"JL Rocha","year":"2013","unstructured":"Rocha, J.L., Fournier-Prunaret, D., Taha, A.-K.: Strong and weak Allee effects and chaotic dynamics in Richards\u2019 growths. Discret. Contin. Dyn. Syst. Ser. B 18(9), 2397\u20132425 (2013)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"key":"1415_CR15","doi-asserted-by":"crossref","DOI":"10.1142\/0413","volume-title":"Chaotic Dynamics from the One-Dimensional Endomorphism to the Two-Dimensional Diffeomorphism","author":"C Mira","year":"1987","unstructured":"Mira, C.: Chaotic Dynamics from the One-Dimensional Endomorphism to the Two-Dimensional Diffeomorphism. World Scientific, Singapore (1987)"},{"key":"1415_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-78043-1","volume-title":"One-Dimensional Dynamics","author":"W Melo","year":"1993","unstructured":"Melo, W., van Strien, S.: One-Dimensional Dynamics. Springer, New York (1993)"},{"key":"1415_CR17","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1137\/0135020","volume":"35","author":"D Singer","year":"1978","unstructured":"Singer, D.: Stable orbits and bifurcations of maps of the interval. SIAM J. Appl. Math. 35, 260\u2013267 (1978)","journal-title":"SIAM J. Appl. Math."},{"key":"1415_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8897-3","volume-title":"Dynamics of One-Dimensional Maps","author":"AN Sharkovsky","year":"1997","unstructured":"Sharkovsky, A.N., Kolyada, S.F., Sivak, A.G., Fedorenko, V.V.: Dynamics of One-Dimensional Maps. Kluwer Academic Publishers, Dordrecht (1997)"},{"issue":"2","key":"1415_CR19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.3934\/mbe.2013.10.379","volume":"10","author":"JL Rocha","year":"2013","unstructured":"Rocha, J.L., Aleixo, S.M.: An extension of gompertzian growth dynamics: Weibull and Fr\u00e9chet models. Math. Biosci. Eng. 10(2), 379\u2013398 (2013)","journal-title":"Math. Biosci. Eng."},{"key":"1415_CR20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF02433474","volume":"6","author":"M Gyllenberg","year":"1996","unstructured":"Gyllenberg, M., Osipov, A.V., Soderbacka, G.: Bifurcation analysis of a metapopulation model with sources and sinks. J. Nonlinear Sci. 6, 329\u2013366 (1996)","journal-title":"J. Nonlinear Sci."},{"key":"1415_CR21","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s002850000070","volume":"42","author":"S Schreiber","year":"2001","unstructured":"Schreiber, S.: Chaos and population disappearances in simple ecological models. J. Math. Biol. 42, 239\u2013260 (2001)","journal-title":"J. Math. Biol."},{"key":"1415_CR22","doi-asserted-by":"crossref","DOI":"10.1142\/2252","volume-title":"Chaotic Dynamics in Two-Dimensional Noninvertible Maps","author":"C Mira","year":"1996","unstructured":"Mira, C., Gardini, L., Barugola, A., Cathala, J.-C.: Chaotic Dynamics in Two-Dimensional Noninvertible Maps. World Scientific, Singapore (1996)"},{"key":"1415_CR23","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1142\/S0218127491000609","volume":"1","author":"D Fournier-Prunaret","year":"1991","unstructured":"Fournier-Prunaret, D.: The bifurcation structure of a family of degree one circle endomorphisms. Int. J. Bifurc. Chaos 1, 823\u2013838 (1991)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1415_CR24","volume-title":"Sur Quelques Structures Complexes de Bifurcations de Systemes Dynamiques","author":"J-P Carcasses","year":"1990","unstructured":"Carcasses, J.-P.: Sur Quelques Structures Complexes de Bifurcations de Systemes Dynamiques. Doctorat de L\u2019Universite Paul Sabatier, INSA, Toulouse (1990)"},{"key":"1415_CR25","unstructured":"Avrutin, V., Wackenhut, G., Schanz, M.: On dynamical systems with piecewise defined system functions. In: Proceedings of International Conference on Tools for Mathematical Modelling (Mathtols\u201999), St. Petersburg, pp. 4\u201320 (1999)"},{"key":"1415_CR26","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1088\/0951-7715\/19\/3\/001","volume":"19","author":"V Avrutin","year":"2006","unstructured":"Avrutin, V., Schanz, M.: Multi-parametric bifurcations in a scalar piecewise-linear map. Nonlinearity 19, 531\u2013552 (2006)","journal-title":"Nonlinearity"},{"key":"1415_CR27","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1088\/0951-7715\/19\/8\/007","volume":"19","author":"V Avrutin","year":"2006","unstructured":"Avrutin, V., Schanz, M., Banerjee, S.: Multi-parametric bifurcations in a piecewise-linear discontinuous map. Nonlinearity 19, 1875\u20131906 (2006)","journal-title":"Nonlinearity"},{"key":"1415_CR28","doi-asserted-by":"crossref","first-page":"2575","DOI":"10.1088\/0951-7715\/24\/9\/012","volume":"24","author":"V Avrutin","year":"2011","unstructured":"Avrutin, V., Granados, A., Schanz, M.: Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional map. Nonlinearity 24, 2575\u20132598 (2011)","journal-title":"Nonlinearity"},{"key":"1415_CR29","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jebo.2011.03.004","volume":"80","author":"L Gardini","year":"2011","unstructured":"Gardini, L., Merlone, U., Tramontana, F.: Inertia in binary choices: continuity breaking and big-bang bifurcation points. J. Econ. Behav. Organ. 80, 153\u2013167 (2011)","journal-title":"J. Econ. Behav. Organ."},{"key":"1415_CR30","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1142\/S0218127409022877","volume":"19","author":"C Mira","year":"2009","unstructured":"Mira, C., Gardini, L.: From the box-within-a-box bifurcation organization to the Julia set. Part I: revisited properties of the sets generated by a quadratic complex map with a real parameter. Int. J. Bifurc. Chaos 19, 281\u2013327 (2009)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1415_CR31","unstructured":"Mira, C.: On some codimension three bifurcations occurring in maps. Spring area-crossroad area transitions. In: Proceedings of European Conference on Iteration Theory (ECIT 1991), Lampreia, J.P., Llibre, J., et al. (Eds.), World Scientific, Singapore, pp. 168\u2013177 (1992)"}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-014-1415-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11071-014-1415-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-014-1415-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T16:38:34Z","timestamp":1689179914000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11071-014-1415-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,4]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["1415"],"URL":"https:\/\/doi.org\/10.1007\/s11071-014-1415-0","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,4]]}}}