{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:10:16Z","timestamp":1774368616221,"version":"3.50.1"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"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":["Evol. Intel."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s12065-023-00835-1","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T18:41:13Z","timestamp":1675881673000},"page":"1425-1435","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A neural network approach for the solution of Van der Pol-Mathieu-Duffing oscillator model"],"prefix":"10.1007","volume":"17","author":[{"given":"Arup Kumar","family":"Sahoo","sequence":"first","affiliation":[]},{"given":"S.","family":"Chakraverty","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"key":"835_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119585640","volume-title":"Mathematical methods in interdisciplinary sciences","author":"S Chakraverty","year":"2020","unstructured":"Chakraverty S (2020) Mathematical methods in interdisciplinary sciences. Wiley, New York"},{"issue":"4","key":"835_CR2","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/BF02478259","volume":"5","author":"WS Mcculloch","year":"1943","unstructured":"Mcculloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115\u2013133","journal-title":"Bull Math Biophys"},{"issue":"1","key":"835_CR3","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/0021-9991(90)90007-N","volume":"91","author":"H Lee","year":"1990","unstructured":"Lee H, Kang IS (1990) Neural algorithm for solving differential equations. J Comput Phys 91(1):110\u2013131. https:\/\/doi.org\/10.1016\/0021-9991(90)90007-N","journal-title":"J Comput Phys"},{"key":"835_CR4","doi-asserted-by":"publisher","unstructured":"Lagaris IE, Likas AC, Papageorgiou DG (2000) Neural-network methods for boundary value problems with irregular boundaries. In: IEEE transactions on Neural Networks, vol 11, no. 5, pp. 1041\u20131049. https:\/\/doi.org\/10.1109\/72.870037","DOI":"10.1109\/72.870037"},{"key":"835_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2013\/181895","volume":"2013","author":"S Mall","year":"2013","unstructured":"Mall S, Chakraverty S (2013) Comparison of artificial neural network architecture in solving ordinary differential equations. Adv Artif Neural Syst 2013:1\u201312. https:\/\/doi.org\/10.1155\/2013\/181895","journal-title":"Adv Artif Neural Syst"},{"issue":"2","key":"835_CR6","first-page":"136","volume":"4","author":"S Mall","year":"2013","unstructured":"Mall S, Chakraverty S (2013) Regression-based neural network training for the solution of ordinary differential equations. Int J Math Modell Numer Optim 4(2):136\u2013149","journal-title":"Int J Math Modell Numer Optim"},{"key":"835_CR7","doi-asserted-by":"publisher","DOI":"10.1201\/9781315155265","volume-title":"Artificial neural networks for engineers and scientists","author":"S Chakraverty","year":"2017","unstructured":"Chakraverty S, Mall S (2017) Artificial neural networks for engineers and scientists. Taylor and Francis, CRC Press, Boca Raton"},{"issue":"4","key":"835_CR8","doi-asserted-by":"publisher","first-page":"2989","DOI":"10.1007\/s00366-020-00985-1","volume":"37","author":"S Panghal","year":"2021","unstructured":"Panghal S, Kumar M (2021) Optimization free neural network approach for solving ordinary and partial differential equations. Eng Comput 37(4):2989\u20133002. https:\/\/doi.org\/10.1007\/s00366-020-00985-1","journal-title":"Eng Comput"},{"key":"835_CR9","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/J.JPROCONT.2019.05.001","volume":"80","author":"XJ Lu","year":"2019","unstructured":"Lu XJ, He PZ, Xu J (2019) Error compensation-based time-space separation modeling method for complex distributed parameter processes. J Process Control 80:117\u2013126. https:\/\/doi.org\/10.1016\/J.JPROCONT.2019.05.001","journal-title":"J Process Control"},{"issue":"2","key":"835_CR10","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/J.ENGAPPAI.2004.02.002","volume":"17","author":"H Niska","year":"2004","unstructured":"Niska H, Hiltunen T, Karppinen A, Ruuskanen J, Kolehmainen M (2004) Evolving the neural network model for forecasting air pollution time series. Eng Appl Artif Intell 17(2):159\u2013167. https:\/\/doi.org\/10.1016\/J.ENGAPPAI.2004.02.002","journal-title":"Eng Appl Artif Intell"},{"key":"835_CR11","doi-asserted-by":"publisher","unstructured":"Salehizadeh SMA, Yadmellat P, Menhaj MB (2009) Local optima avoidable particle swarm optimization. In: 2009 IEEE Swarm Intelligence Symposium, SIS 2009\u2014Proceedings, 2009, pp. 16\u201321. https:\/\/doi.org\/10.1109\/SIS.2009.4937839.","DOI":"10.1109\/SIS.2009.4937839"},{"key":"835_CR12","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1016\/J.JCP.2018.08.029","volume":"375","author":"J Sirignano","year":"2018","unstructured":"Sirignano J, Spiliopoulos K (2018) DGM: a deep learning algorithm for solving partial differential equations. J Comput Phys 375:1339\u20131364. https:\/\/doi.org\/10.1016\/J.JCP.2018.08.029","journal-title":"J Comput Phys"},{"key":"835_CR13","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0895-7177(94)00160-X","volume":"20","author":"AJ Meade Jr","year":"1994","unstructured":"Meade AJ Jr, Fernandez AA (1994) Solution of nonlinear ordinary differential equations by feed forward neural networks. Math Comput Model 20:19\u201344","journal-title":"Math Comput Model"},{"issue":"4","key":"835_CR14","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s12065-020-00383-y","volume":"13","author":"S Chakraverty","year":"2020","unstructured":"Chakraverty S, Mall S (2020) Single layer Chebyshev neural network model with regression-based weights for solving nonlinear ordinary differential equations. Evol Intel 13(4):687\u2013694. https:\/\/doi.org\/10.1007\/s12065-020-00383-y","journal-title":"Evol Intel"},{"key":"835_CR15","doi-asserted-by":"publisher","unstructured":"Verma A, Kumar M (2020) Numerical solution of third-order Emden\u2013Fowler type equations using artificial neural network technique. Euro Phys J Plus 135(9). https:\/\/doi.org\/10.1140\/epjp\/s13360-020-00780-3.","DOI":"10.1140\/epjp\/s13360-020-00780-3"},{"issue":"1","key":"835_CR16","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s12065-020-00497-3","volume":"15","author":"RM Rizk-Allah","year":"2022","unstructured":"Rizk-Allah RM, Hassanien AE (2022) A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations. Evol Intel 15(1):141\u2013165. https:\/\/doi.org\/10.1007\/s12065-020-00497-3","journal-title":"Evol Intel"},{"key":"835_CR17","doi-asserted-by":"publisher","unstructured":"Motsa SS, Sibanda P (2012) A note on the solutions of the van der pol and duffing equations using a linearisation method. Math Problems Eng. https:\/\/doi.org\/10.1155\/2012\/693453.","DOI":"10.1155\/2012\/693453"},{"issue":"5","key":"835_CR18","doi-asserted-by":"publisher","first-page":"1356","DOI":"10.1016\/j.chaos.2006.10.038","volume":"37","author":"AN Njah","year":"2008","unstructured":"Njah AN, Vincent UE (2008) Chaos synchronization between single and double wells Duffing-Van der Pol oscillators using active control. Chaos Solitons Fractals 37(5):1356\u20131361. https:\/\/doi.org\/10.1016\/j.chaos.2006.10.038","journal-title":"Chaos Solitons Fractals"},{"key":"835_CR19","doi-asserted-by":"publisher","unstructured":"Ibsen LB, Barari A, Kimiaeifar A (2010) Analysis of highly nonlinear oscillation systems using He\u2019s max-min method and comparison with homotopy analysis and energy balance methods. Sadhana 35:433\u2013448. https:\/\/doi.org\/10.1007\/s12046-010-0024-y","DOI":"10.1007\/s12046-010-0024-y"},{"issue":"2","key":"835_CR20","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.scient.2013.02.023","volume":"20","author":"S Nourazar","year":"2013","unstructured":"Nourazar S, Mirzabeigy A (2013) Approximate solution for nonlinear Duffing oscillator with damping effect using the modified differential transform method. Scientia Iranica 20(2):364\u2013368. https:\/\/doi.org\/10.1016\/j.scient.2013.02.023","journal-title":"Scientia Iranica"},{"key":"835_CR21","doi-asserted-by":"publisher","unstructured":"Hu K, Chung K (2013) On the stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings. AIP Adv 3(1):112118. https:\/\/doi.org\/10.1063\/1.4834115.","DOI":"10.1063\/1.4834115"},{"key":"835_CR22","doi-asserted-by":"publisher","unstructured":"Akbari M (2018) Nonlinear dynamical structures on coupled Duffing-Van der Pol Oscillators with two degrees of freedom by new approach AGM.  Res Dev Mater Sci 7(4). https:\/\/doi.org\/10.31031\/RDMS.2018.07.000670.","DOI":"10.31031\/RDMS.2018.07.000670"},{"issue":"13","key":"835_CR23","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1002\/mma.1269","volume":"33","author":"A Kimiaeifar","year":"2010","unstructured":"Kimiaeifar A (2010) An analytical approach to investigate the response and stability of Van der Pol-Mathieu-Duffing oscillators under different excitation functions. Math Methods Appl Sci 33(13):1571\u20131577. https:\/\/doi.org\/10.1002\/mma.1269","journal-title":"Math Methods Appl Sci"},{"key":"835_CR24","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/J.AMC.2014.01.161","volume":"234","author":"J Kalas","year":"2014","unstructured":"Kalas J, Kade\u0159\u00e1bek Z (2014) Periodic solutions of a generalized Van der Pol-Mathieu differential equation. Appl Math Comput 234:192\u2013202. https:\/\/doi.org\/10.1016\/J.AMC.2014.01.161","journal-title":"Appl Math Comput"},{"key":"835_CR25","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1016\/J.CNSNS.2016.02.003","volume":"37","author":"X Li","year":"2016","unstructured":"Li X, Hou J, Chen J (2016) An analytical method for Mathieu oscillator based on method of variation of parameter. Commun Nonlinear Sci Numer Simul 37:326\u2013353. https:\/\/doi.org\/10.1016\/J.CNSNS.2016.02.003","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"835_CR26","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1515\/ijnsns-2015-0012","volume":"17","author":"Q Fan","year":"2016","unstructured":"Fan Q, Leung AYT, Lee YY (Feb.2016) Periodic and quasi-periodic responses of Van der Pol-Mathieu system subject to various excitations. Int J Nonlinear Sci Numer Simulat 17(1):29\u201340. https:\/\/doi.org\/10.1515\/ijnsns-2015-0012","journal-title":"Int J Nonlinear Sci Numer Simulat"},{"key":"835_CR27","doi-asserted-by":"publisher","unstructured":"Jadoon I, Raja MAZ, Junaid M, Ahmed A, ur Rehman A, Shoaib M (2021) Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu\u2019s oscillatory systems. Math Comp Simulation 181:444\u2013470. https:\/\/doi.org\/10.1016\/j.matcom.2020.10.004.","DOI":"10.1016\/j.matcom.2020.10.004"},{"issue":"1","key":"835_CR28","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1137\/19M1274067","volume":"63","author":"L Lu","year":"2021","unstructured":"Lu L, Meng X, Mao Z, Karniadakis GE (2021) DeepXDE: Aa deep learning library for solving differential equations. SIAM Rev 63(1):208\u2013228. https:\/\/doi.org\/10.1137\/19M1274067","journal-title":"SIAM Rev"},{"key":"835_CR29","doi-asserted-by":"publisher","unstructured":"Chen F et al (2020) NeuroDiffEq: A Python package for solving differential equations with neural networks. J  Open Source Softw 5(46):1931. https:\/\/doi.org\/10.21105\/joss.01931.","DOI":"10.21105\/joss.01931"},{"key":"835_CR30","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/j.asoc.2017.10.049","volume":"62","author":"MAZ Raja","year":"2018","unstructured":"Raja MAZ, Manzar MA, Shah FH, Shah FH (2018) Intelligent computing for Mathieu\u2019s systems for parameter excitation, vertically driven pendulum and dusty plasma models. Appl Soft Comput J 62:359\u2013372","journal-title":"Appl Soft Comput J"},{"key":"835_CR31","doi-asserted-by":"publisher","unstructured":"Wang K, Yan X, Yang Q, Hao X, Wang J (2020) Weak signal detection based on strongly coupled Duffing-Van der Pol oscillator and long short-term memory. J Phys Soc Japan 89(1):014003. https:\/\/doi.org\/10.7566\/JPSJ.89.014003.","DOI":"10.7566\/JPSJ.89.014003"},{"key":"835_CR32","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.neucom.2020.02.022","volume":"399","author":"KL Yin","year":"2020","unstructured":"Yin KL, Pu YF, Lu L (2020) Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator. Neurocomputing 399:183\u2013192. https:\/\/doi.org\/10.1016\/j.neucom.2020.02.022","journal-title":"Neurocomputing"},{"issue":"5","key":"835_CR33","doi-asserted-by":"publisher","first-page":"3325","DOI":"10.1016\/j.aej.2020.04.051","volume":"59","author":"AH Bukhari","year":"2020","unstructured":"Bukhari AH, Sulaiman M, Raja MAZ, Islam S, Shoaib M, Kumam P (2020) Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system. Alex Eng J 59(5):3325\u20133345","journal-title":"Alex Eng J"},{"key":"835_CR34","unstructured":"Mattheakis M, Protopapas P, Sondak D, di Giovanni M, Kaxiras E (2019) Physical symmetries embedded in neural networks [Online]. Available: http:\/\/arxiv.org\/abs\/1904.08991"},{"key":"835_CR35","doi-asserted-by":"publisher","unstructured":"Sahoo AK, Chakraverty S (2022) Curriculum learning-based artificial neural network model for solving differential equations. In: Chakraverty S (ed) Studies in Computational Intelligence, 1st edn, vol. 988. Springer, Singapore. https:\/\/doi.org\/10.1007\/978-981-16-4713-0_6.","DOI":"10.1007\/978-981-16-4713-0_6"},{"key":"835_CR36","volume-title":"Introduction to Artificial Neural Systems","author":"JM Zurada","year":"1992","unstructured":"Zurada JM (1992) Introduction to Artificial Neural Systems. West Publishing Co., USA"},{"key":"835_CR37","doi-asserted-by":"publisher","unstructured":"Chakraverty S, Jeswal SK (2021) Applied artificial neural network methods for engineers and scientists. World Scientific, Singapore. https:\/\/doi.org\/10.1142\/12097.","DOI":"10.1142\/12097"},{"key":"835_CR38","doi-asserted-by":"publisher","unstructured":"Chakraverty S, Sahoo DM, Mahato NR (2019) Concepts of soft computing. Springer, Singapore. https:\/\/doi.org\/10.1007\/978-981-13-7430-2.","DOI":"10.1007\/978-981-13-7430-2"},{"key":"835_CR39","doi-asserted-by":"crossref","unstructured":"Pippard A (1987) The inverted pendulum. Euro J Phys 8(3).","DOI":"10.1088\/0143-0807\/8\/3\/012"},{"key":"835_CR40","doi-asserted-by":"publisher","unstructured":"Sadat Kiai SM (1999) Confinement of ions in a radio frequency quadrupole ion trap supplied with a periodic impulsional potential. Int J Mass Spectrometry 188(3):177\u2013182. https:\/\/doi.org\/10.1016\/S1387-3806(99)00019-6.","DOI":"10.1016\/S1387-3806(99)00019-6"},{"issue":"5","key":"835_CR41","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1016\/S0022-460X(03)00002-6","volume":"268","author":"NQ Hu","year":"2003","unstructured":"Hu NQ, Wen XS (2003) The application of Duffing oscillator in characteristic signal detection of early fault. J Sound Vib 268(5):917\u2013931. https:\/\/doi.org\/10.1016\/S0022-460X(03)00002-6","journal-title":"J Sound Vib"},{"issue":"1\u20136","key":"835_CR42","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0030-4018(03)01564-5","volume":"222","author":"CA Dartora","year":"2003","unstructured":"Dartora CA, Zamboni-Rached M, N\u00f3brega KZ, Recami E, Hern\u00e1ndez-Figueroa HE (2003) General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams. Optics Communications 222(1\u20136):75\u201380. https:\/\/doi.org\/10.1016\/S0030-4018(03)01564-5","journal-title":"Optics Communications"},{"key":"835_CR43","doi-asserted-by":"publisher","unstructured":"Zhihong Z, Shaopu Y, Tan ZH (2015) Application of van der Pol\u2013Duffing oscillator in weak signal detection. Comp Electrical Eng 41(C):1\u20138. https:\/\/doi.org\/10.1016\/J.COMPELECENG.2014.11.007.","DOI":"10.1016\/J.COMPELECENG.2014.11.007"},{"issue":"1\u20132","key":"835_CR44","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s11071-007-9238-x","volume":"54","author":"M Pandey","year":"2008","unstructured":"Pandey M, Rand RH, Zehnder AT (2008) Frequency locking in a forced Mathieu-van der Pol-Duffing system. Nonlinear Dyn 54(1\u20132):3\u201312. https:\/\/doi.org\/10.1007\/s11071-007-9238-x","journal-title":"Nonlinear Dyn"},{"key":"835_CR45","volume-title":"Deep learning","author":"I Goodfellow","year":"2016","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT press, Cambridge"},{"key":"835_CR46","doi-asserted-by":"publisher","unstructured":"Jesus RJ, Antunes ML, da Costa RA, Dorogovtsev SA, Mendes JFF, Aguiar RL (2021) Effect of initial configuration of weights on training and function of artificial neural networks. Mathematics 9(18). https:\/\/doi.org\/10.3390\/math9182246.","DOI":"10.3390\/math9182246"},{"key":"835_CR47","unstructured":"Ramachandran B, Zoph B, Le Qv (2017) Searching for activation functions. [Online]. Available: http:\/\/arxiv.org\/abs\/1710.05941"},{"key":"835_CR48","doi-asserted-by":"publisher","unstructured":"Umar M, Amin F, Wahab HA, Baleanu D (2019) Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery. Appl Soft Comput J 85. https:\/\/doi.org\/10.1016\/j.asoc.2019.105826.","DOI":"10.1016\/j.asoc.2019.105826"},{"key":"835_CR49","doi-asserted-by":"publisher","DOI":"10.1002\/widm.1461","author":"AK Sahoo","year":"2022","unstructured":"Sahoo AK, Chakraverty S (2022) Machine intelligence in dynamical systems: a state-of-art review. WIREs Data Min Knowl Discovery. https:\/\/doi.org\/10.1002\/widm.1461","journal-title":"WIREs Data Min Knowl Discovery"},{"key":"835_CR50","doi-asserted-by":"publisher","unstructured":"Masood Z, Samar R, Raja MAZ (2019) Design of a mathematical model for the Stuxnet virus in a network of critical control infrastructure. Comp Security, 87. https:\/\/doi.org\/10.1016\/j.cose.2019.07.002.","DOI":"10.1016\/j.cose.2019.07.002"},{"key":"835_CR51","doi-asserted-by":"publisher","unstructured":"Guerrero S\u00e1nchez Y, Sabir Z, G\u00fcnerhan H, Baskonus HM (2020) Analytical and approximate solutions of a novel nervous stomach mathematical model. Discrete Dyn Nature Soc, https:\/\/doi.org\/10.1155\/2020\/5063271.","DOI":"10.1155\/2020\/5063271"},{"issue":"4","key":"835_CR52","doi-asserted-by":"publisher","first-page":"2027","DOI":"10.1007\/s12065-020-00481-x","volume":"14","author":"A Verma","year":"2021","unstructured":"Verma A, Kumar M (2021) Numerical solution of Bagley-Torvik equations using Legendre artificial neural network method. Evol Intel 14(4):2027\u20132037. https:\/\/doi.org\/10.1007\/s12065-020-00481-x","journal-title":"Evol Intel"}],"container-title":["Evolutionary Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12065-023-00835-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12065-023-00835-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12065-023-00835-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T12:14:54Z","timestamp":1716293694000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12065-023-00835-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,8]]},"references-count":52,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["835"],"URL":"https:\/\/doi.org\/10.1007\/s12065-023-00835-1","relation":{},"ISSN":["1864-5909","1864-5917"],"issn-type":[{"value":"1864-5909","type":"print"},{"value":"1864-5917","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,8]]},"assertion":[{"value":"6 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors have no conflicts of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}