{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:56:48Z","timestamp":1765486608493,"version":"3.40.3"},"reference-count":63,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s11071-021-06503-2","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T19:02:40Z","timestamp":1621623760000},"page":"3897-3911","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Entropy analysis of human death uncertainty"],"prefix":"10.1007","volume":"104","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"J. A.","family":"Tenreiro Machado","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"issue":"23\u201324","key":"6503_CR1","doi-asserted-by":"publisher","first-page":"1962","DOI":"10.1016\/j.spl.2010.08.026","volume":"80","author":"M Abbasnejad","year":"2010","unstructured":"Abbasnejad, M., Arghami, N.R., Morgenthaler, S., Borzadaran, G.M.: On the dynamic survival entropy. Statist. Probab. Lett. 80(23\u201324), 1962\u20131971 (2010)","journal-title":"Statist. Probab. Lett."},{"key":"6503_CR2","unstructured":"Abdul\u00a0Sathar, E., Nair\u00a0R, D.: On dynamic survival extropy. Commun. Statis-Theory Meth. pp. 1\u201319 (2019)"},{"key":"6503_CR3","doi-asserted-by":"publisher","first-page":"83","DOI":"10.4054\/DemRes.2019.41.4","volume":"41","author":"JM Aburto","year":"2019","unstructured":"Aburto, J.M., Alvarez, J.A., Villavicencio, F., Vaupel, J.W.: The threshold age of the lifetable entropy. Demograp. Res. 41, 83\u2013102 (2019)","journal-title":"Demograp. Res."},{"issue":"10","key":"6503_CR4","doi-asserted-by":"publisher","first-page":"5250","DOI":"10.1073\/pnas.1915884117","volume":"117","author":"JM Aburto","year":"2020","unstructured":"Aburto, J.M., Villavicencio, F., Basellini, U., Kj\u00e6rgaard, S., Vaupel, J.W.: Dynamics of life expectancy and life span equality. Proc. Nat. Acad. Sci. 117(10), 5250\u20135259 (2020)","journal-title":"Proc. Nat. Acad. Sci."},{"issue":"2","key":"6503_CR5","first-page":"319","volume":"14","author":"M Al-Shabi","year":"2020","unstructured":"Al-Shabi, M.: A novel edge detection algorithm based on cumulative residual entropy. Applied Mathematics 14(2), 319\u2013326 (2020)","journal-title":"Applied Mathematics"},{"issue":"6","key":"6503_CR6","doi-asserted-by":"publisher","first-page":"1931","DOI":"10.1016\/j.jspi.2006.06.035","volume":"137","author":"M Asadi","year":"2007","unstructured":"Asadi, M., Zohrevand, Y.: On the dynamic cumulative residual entropy. J. Statist. Plan. Inf. 137(6), 1931\u20131941 (2007)","journal-title":"J. Statist. Plan. Inf."},{"key":"6503_CR7","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A.: Entropy: The truth, the whole truth and nothing but the truth. World Scientific, (2017)","DOI":"10.1142\/10226"},{"key":"6503_CR8","unstructured":"Boltzmann, L.: Vorlesungen \u00fcber die Principe der Mechanik, vol.\u00a01. JA Barth (1897)"},{"key":"6503_CR9","doi-asserted-by":"publisher","first-page":"1012","DOI":"10.1016\/j.physa.2017.05.063","volume":"486","author":"C Cal\u00ec","year":"2017","unstructured":"Cal\u00ec, C., Longobardi, M., Ahmadi, J.: Some properties of cumulative Tsallis entropy. Phys. A 486, 1012\u20131021 (2017)","journal-title":"Phys. A"},{"key":"6503_CR10","unstructured":"Clausius, R.: The mechanical theory of heat: with its applications to the steam-engine and to the physical properties of bodies. J. van Voorst (1867)"},{"key":"6503_CR11","doi-asserted-by":"crossref","unstructured":"Di\u00a0Crescenzo, A., Longobardi, M.: Entropy-based measure of uncertainty in past lifetime distributions. J. Appl. Prob. 434\u2013440 (2002)","DOI":"10.1017\/S002190020002266X"},{"issue":"12","key":"6503_CR12","doi-asserted-by":"publisher","first-page":"4072","DOI":"10.1016\/j.jspi.2009.05.038","volume":"139","author":"A Di Crescenzo","year":"2009","unstructured":"Di Crescenzo, A., Longobardi, M.: On cumulative entropies. J. Statist. Plan. Inf. 139(12), 4072\u20134087 (2009)","journal-title":"J. Statist. Plan. Inf."},{"issue":"1","key":"6503_CR13","doi-asserted-by":"publisher","first-page":"012106","DOI":"10.1103\/PhysRevE.101.012106","volume":"101","author":"YM Du","year":"2020","unstructured":"Du, Y.M., Ma, Y.H., Wei, Y.F., Guan, X., Sun, C.: Maximum entropy approach to reliability. Phys. Rev. E 101(1), 012106 (2020)","journal-title":"Phys. Rev. E"},{"key":"6503_CR14","doi-asserted-by":"crossref","unstructured":"Ebrahimi, N.: How to measure uncertainty in the residual life time distribution. Sankhy\u0101: The Indian J. Statist. Series A, pp. 48\u201356 (1996)","DOI":"10.1007\/BF00054789"},{"issue":"4","key":"6503_CR15","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1111\/j.1728-4457.2005.00092.x","volume":"31","author":"RD Edwards","year":"2005","unstructured":"Edwards, R.D., Tuljapurkar, S.: Inequality in life spans and a new perspective on mortality convergence across industrialized countries. Populat. Develop. Rev. 31(4), 645\u2013674 (2005)","journal-title":"Populat. Develop. Rev."},{"key":"6503_CR16","doi-asserted-by":"crossref","unstructured":"Elsayed, E.A.: Reliability engineering. Wiley (2020)","DOI":"10.1002\/9781119665946"},{"issue":"3","key":"6503_CR17","doi-asserted-by":"publisher","first-page":"331","DOI":"10.2307\/2060621","volume":"8","author":"N Fergany","year":"1971","unstructured":"Fergany, N.: On the human survivorship function and life table construction. Demography 8(3), 331\u2013334 (1971)","journal-title":"Demography"},{"key":"6503_CR18","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.tpb.2015.07.001","volume":"104","author":"OE Fernandez","year":"2015","unstructured":"Fernandez, O.E., Beltr\u00e1n-S\u00e1nchez, H.: The entropy of the life table: A reappraisal. Theor. Popul. Biol. 104, 26\u201345 (2015)","journal-title":"Theor. Popul. Biol."},{"issue":"2","key":"6503_CR19","doi-asserted-by":"publisher","first-page":"275","DOI":"10.2307\/2061621","volume":"23","author":"N Goldman","year":"1986","unstructured":"Goldman, N., Lord, G.: A new look at entropy and the life table. Demography 23(2), 275\u2013282 (1986)","journal-title":"Demography"},{"issue":"4","key":"6503_CR20","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1103\/PhysRev.106.620","volume":"106","author":"ET Jaynes","year":"1957","unstructured":"Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620 (1957)","journal-title":"Phys. Rev."},{"key":"6503_CR21","doi-asserted-by":"crossref","unstructured":"Kamari, O., Buono, F.: On extropy of past lifetime distribution. Ricerche di Matematica, pp. 1\u201311 (2020)","DOI":"10.1007\/s11587-020-00488-7"},{"key":"6503_CR22","doi-asserted-by":"crossref","unstructured":"Kannisto, V.: Measuring the compression of mortality. Demograph. Res. 3, (2000)","DOI":"10.4054\/DemRes.2000.3.6"},{"issue":"1","key":"6503_CR23","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1017\/S0269964811000271","volume":"26","author":"S Kapodistria","year":"2012","unstructured":"Kapodistria, S., Psarrakos, G.: Some extensions of the residual lifetime and its connection to the cumulative residual entropy. Probability in the Engineering and Informational Sciences 26(1), 129 (2012)","journal-title":"Probability in the Engineering and Informational Sciences"},{"issue":"2","key":"6503_CR24","first-page":"153","volume":"20","author":"S Kayal","year":"2017","unstructured":"Kayal, S., Moharana, R.: On weighted cumulative residual entropy. J. Statist. Manag. Syst 20(2), 153\u2013173 (2017)","journal-title":"J. Statist. Manag. Syst"},{"key":"6503_CR25","unstructured":"Keyfitz, N.: Applied mathematical demography. Springer, (2005)"},{"key":"6503_CR26","doi-asserted-by":"crossref","unstructured":"Kleiber, C., Kotz, S.: Statistical size distributions in economics and actuarial sciences, vol. 470. Wiley (2003)","DOI":"10.1002\/0471457175"},{"key":"6503_CR27","doi-asserted-by":"crossref","unstructured":"Kleinbum, D., Klein, M.: Survival analysis: a self-learning text. Springer (2012)","DOI":"10.1007\/978-1-4419-6646-9"},{"issue":"1","key":"6503_CR28","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1080\/00324720601103833","volume":"61","author":"S Lan Karen Cheung","year":"2007","unstructured":"Lan Karen Cheung, S., Robine, J.M.: Increase in common longevity and the compression of mortality: the case of Japan. Populat. Stud. 61(1), 85\u201397 (2007)","journal-title":"Populat. Stud."},{"issue":"1","key":"6503_CR29","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1080\/10920277.2007.10597438","volume":"11","author":"SH Li","year":"2007","unstructured":"Li, S.H., Chan, W.S.: The lee-carter model for forecasting mortality, revisited. North Am. Act. J. 11(1), 68\u201389 (2007)","journal-title":"North Am. Act. J."},{"issue":"12","key":"6503_CR30","doi-asserted-by":"publisher","first-page":"1374","DOI":"10.3390\/e22121374","volume":"22","author":"AM Lopes","year":"2020","unstructured":"Lopes, A.M., Machado, J.A.T.: A review of fractional order entropies. Entropy 22(12), 1374 (2020)","journal-title":"Entropy"},{"key":"6503_CR31","doi-asserted-by":"crossref","unstructured":"Macdonald, A.S., Richards, S.J., Currie, I.D.: Modelling mortality with actuarial applications. Cambridge University Press (2018)","DOI":"10.1017\/9781107051386"},{"issue":"1","key":"6503_CR32","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s11071-014-1645-1","volume":"79","author":"JT Machado","year":"2015","unstructured":"Machado, J.T., Lopes, A.M.: The persistence of memory. Nonlinear Dyn. 79(1), 63\u201382 (2015)","journal-title":"Nonlinear Dyn."},{"key":"6503_CR33","doi-asserted-by":"publisher","first-page":"2953","DOI":"10.1007\/s11071-020-05680-w","volume":"100","author":"JT Machado","year":"2020","unstructured":"Machado, J.T., Lopes, A.M.: Rare and extreme events: the case of COVID-19 pandemic. Nonlinear Dyn. 100, 2953\u20132972 (2020)","journal-title":"Nonlinear Dyn."},{"issue":"1","key":"6503_CR34","first-page":"129","volume":"14","author":"P Meyer","year":"2020","unstructured":"Meyer, P., Ponthi\u00e8re, G.: Human lifetime entropy in a historical perspective (1750\u20132014). Cliometrica 14(1), 129\u2013167 (2020)","journal-title":"Cliometrica"},{"key":"6503_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.mathsocsci.2020.07.004","volume":"108","author":"P Meyer","year":"2020","unstructured":"Meyer, P., Ponthiere, G.: Threshold ages for the relation between lifetime entropy and mortality risk. Mathem. Soc. Sci. 108, 1\u20137 (2020)","journal-title":"Mathem. Soc. Sci."},{"issue":"6","key":"6503_CR36","doi-asserted-by":"publisher","first-page":"2816","DOI":"10.1080\/03610926.2015.1053928","volume":"46","author":"S Minimol","year":"2017","unstructured":"Minimol, S.: On generalized dynamic cumulative past entropy measure. Commun. Statist. Theory Meth. 46(6), 2816\u20132822 (2017)","journal-title":"Commun. Statist. Theory Meth."},{"key":"6503_CR37","doi-asserted-by":"crossref","unstructured":"Nagnur, D.: Rectangularization of the survival curve and entropy: The Canadian experience, 1921-1981. Canadian Studies in Population [ARCHIVES], pp. 83\u2013102 (1986)","DOI":"10.25336\/P6QG6M"},{"key":"6503_CR38","unstructured":"Namboodiri, K., Suchindran, C.M.: Life table techniques and their applications. Academic Press, (2013)"},{"issue":"1","key":"6503_CR39","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.jspi.2009.07.015","volume":"140","author":"J Navarro","year":"2010","unstructured":"Navarro, J., del Aguila, Y., Asadi, M.: Some new results on the cumulative residual entropy. J. Statist. Plan. Inf. 140(1), 310\u2013322 (2010)","journal-title":"J. Statist. Plan. Inf."},{"issue":"3","key":"6503_CR40","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1080\/03610926.2015.1014111","volume":"46","author":"J Navarro","year":"2017","unstructured":"Navarro, J., Psarrakos, G.: Characterizations based on generalized cumulative residual entropy functions. Commun. Statist. Theory Meth. 46(3), 1247\u20131260 (2017)","journal-title":"Commun. Statist. Theory Meth."},{"issue":"4","key":"6503_CR41","doi-asserted-by":"publisher","first-page":"911","DOI":"10.2478\/s13540-013-0056-1","volume":"16","author":"R Nigmatullin","year":"2013","unstructured":"Nigmatullin, R., Baleanu, D.: New relationships connecting a class of fractal objects and fractional integrals in space. Fract. Calculus Appl. Analy. 16(4), 911\u2013936 (2013)","journal-title":"Fract. Calculus Appl. Analy."},{"issue":"14","key":"6503_CR42","doi-asserted-by":"publisher","first-page":"7085","DOI":"10.1080\/03610926.2016.1148729","volume":"46","author":"M Nourbakhsh","year":"2017","unstructured":"Nourbakhsh, M., Yari, G.: Weighted Renyi\u2019s entropy for lifetime distributions. Commun. Statist.Theory Meth. 46(14), 7085\u20137098 (2017)","journal-title":"Commun. Statist.Theory Meth."},{"issue":"10","key":"6503_CR43","doi-asserted-by":"publisher","first-page":"e0223789","DOI":"10.1371\/journal.pone.0223789","volume":"14","author":"M Postigo-Boix","year":"2019","unstructured":"Postigo-Boix, M., Ag\u00fcero, R., Mel\u00fas-Moreno, J.L.: An alternative procedure to obtain the mortality rate with non-linear functions: Application to the case of the Spanish population. PLoS ONE 14(10), e0223789 (2019)","journal-title":"PLoS ONE"},{"issue":"5","key":"6503_CR44","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1007\/s00184-012-0408-6","volume":"76","author":"G Psarrakos","year":"2013","unstructured":"Psarrakos, G., Navarro, J.: Generalized cumulative residual entropy and record values. Metrika 76(5), 623\u2013640 (2013)","journal-title":"Metrika"},{"key":"6503_CR45","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.cam.2016.06.037","volume":"309","author":"G Psarrakos","year":"2017","unstructured":"Psarrakos, G., Toomaj, A.: On the generalized cumulative residual entropy with applications in actuarial science. J. Comput. Appl. Math. 309, 186\u2013199 (2017)","journal-title":"J. Comput. Appl. Math."},{"issue":"6","key":"6503_CR46","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1109\/TIT.2004.828057","volume":"50","author":"M Rao","year":"2004","unstructured":"Rao, M., Chen, Y., Vemuri, B.C., Wang, F.: Cumulative residual entropy: a new measure of information. IEEE Trans. Inf. Theory 50(6), 1220\u20131228 (2004)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"6503_CR47","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1093\/oxfordjournals.aje.a117382","volume":"141","author":"LJ Reed","year":"1995","unstructured":"Reed, L.J., Merrell, M.: A short method for constructing an abridged life table. Am. J. Epidemiol. 141(11), 993\u20131022 (1995)","journal-title":"Am. J. Epidemiol."},{"issue":"1","key":"6503_CR48","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s11009-012-9300-0","volume":"16","author":"A Sachlas","year":"2014","unstructured":"Sachlas, A., Papaioannou, T.: Residual and past entropy in actuarial science and survival models. Methodol. Comput. Appl. Prob. 16(1), 79\u201399 (2014)","journal-title":"Methodol. Comput. Appl. Prob."},{"issue":"11","key":"6503_CR49","first-page":"1","volume":"4","author":"P Saikia","year":"2013","unstructured":"Saikia, P., Borah, M.: A study on mathematical modelling for oldest-old mortality rates. Int. J. Mathem. Archive (IJMA) 4(11), 1\u20139 (2013)","journal-title":"Int. J. Mathem. Archive (IJMA)"},{"key":"6503_CR50","doi-asserted-by":"crossref","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379\u2013423, 623\u2013656 (1948)","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"issue":"3","key":"6503_CR51","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379\u2013423 (1948)","journal-title":"Bell Syst. Tech. J."},{"issue":"06","key":"6503_CR52","doi-asserted-by":"publisher","first-page":"683","DOI":"10.4236\/tel.2015.56079","volume":"5","author":"A Sinha","year":"2015","unstructured":"Sinha, A., Rastogi, S.K., et al.: Inequality in access to improved water source: A regional analysis by Theil Index. Theoretical Economics Letters 5(06), 683 (2015)","journal-title":"Theoretical Economics Letters"},{"issue":"6","key":"6503_CR53","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1016\/j.socscimed.2008.12.034","volume":"68","author":"J Smits","year":"2009","unstructured":"Smits, J., Monden, C.: Length of life inequality around the globe. Soc. Sci. Med. 68(6), 1114\u20131123 (2009)","journal-title":"Soc. Sci. Med."},{"issue":"11","key":"6503_CR54","first-page":"1580","volume":"11","author":"VE Tarasov","year":"2013","unstructured":"Tarasov, V.E.: Lattice model with power-law spatial dispersion for fractional elasticity. Cent. Eur. J. Phys. 11(11), 1580\u20131588 (2013)","journal-title":"Cent. Eur. J. Phys."},{"issue":"6","key":"6503_CR55","doi-asserted-by":"publisher","first-page":"709","DOI":"10.3390\/e22060709","volume":"22","author":"A Toomaj","year":"2020","unstructured":"Toomaj, A., Di Crescenzo, A.: Generalized entropies, variance and applications. Entropy 22(6), 709 (2020)","journal-title":"Entropy"},{"issue":"5","key":"6503_CR56","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1007\/s13524-013-0223-3","volume":"50","author":"AA Van Raalte","year":"2013","unstructured":"Van Raalte, A.A., Caswell, H.: Perturbation analysis of indices of lifespan variability. Demography 50(5), 1615\u20131640 (2013)","journal-title":"Demography"},{"issue":"1","key":"6503_CR57","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1080\/0032472031000141896","volume":"40","author":"JW Vaupel","year":"1986","unstructured":"Vaupel, J.W.: How change in age-specific mortality affects life expectancy. Populat. Stud. 40(1), 147\u2013157 (1986)","journal-title":"Populat. Stud."},{"issue":"2","key":"6503_CR58","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1353\/dem.2003.0018","volume":"40","author":"JW Vaupel","year":"2003","unstructured":"Vaupel, J.W., Romo, V.C.: Decomposing change in life expectancy: a bouquet of formulas in honor of Nathan Keyfitz\u2019s 90th birthday. Demography 40(2), 201\u2013216 (2003)","journal-title":"Demography"},{"issue":"2","key":"6503_CR59","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s11263-006-0011-2","volume":"74","author":"F Wang","year":"2007","unstructured":"Wang, F., Vemuri, B.C.: Non-rigid multi-modal image registration using cross-cumulative residual entropy. Int. J. Comput. Vision 74(2), 201\u2013215 (2007)","journal-title":"Int. J. Comput. Vision"},{"key":"6503_CR60","doi-asserted-by":"crossref","unstructured":"Wilmoth, J.R., Horiuchi, S.: Rectangularization revisited: variability of age at death within human populations. Demography 36(4), 475\u2013495 (1999)","DOI":"10.2307\/2648085"},{"key":"6503_CR61","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.insmatheco.2015.08.006","volume":"65","author":"CH Wong","year":"2015","unstructured":"Wong, C.H., Tsui, A.K.: Forecasting life expectancy: evidence from a new survival function. Insu. Mathem. Econ. 65, 208\u2013226 (2015)","journal-title":"Insu. Mathem. Econ."},{"key":"6503_CR62","doi-asserted-by":"publisher","first-page":"721","DOI":"10.4054\/DemRes.2009.20.29","volume":"20","author":"Z Zhang","year":"2009","unstructured":"Zhang, Z., Vaupel, J.W.: The age separating early deaths from late deaths. Demograp. Res. 20, 721\u2013730 (2009)","journal-title":"Demograp. Res."},{"issue":"2","key":"6503_CR63","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1198\/tech.2006.s408","volume":"48","author":"ER Ziegel","year":"2006","unstructured":"Ziegel, E.R.: Survival analysis: a self-learning text. Technometrics 48(2), 317 (2006)","journal-title":"Technometrics"}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-021-06503-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11071-021-06503-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-021-06503-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T06:13:47Z","timestamp":1744092827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11071-021-06503-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,21]]},"references-count":63,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["6503"],"URL":"https:\/\/doi.org\/10.1007\/s11071-021-06503-2","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"type":"print","value":"0924-090X"},{"type":"electronic","value":"1573-269X"}],"subject":[],"published":{"date-parts":[[2021,5,21]]},"assertion":[{"value":"10 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2021","order":3,"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 conflict of interest","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}