{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T22:05:20Z","timestamp":1778623520392,"version":"3.51.4"},"reference-count":23,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T00:00:00Z","timestamp":1601856000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,10,5]]},"abstract":"<jats:p>This paper deals with the effects of an amplitude-modulated (AM) excitation on the nonlinear dynamics of reactions between four molecules. The computation of the \ufb01xed points of the autonomous nonlinear chemical system has been made in detail using the Cardan\u2019s method. Hopf bifurcation has been also successfully checked. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent, phase portraits, and Poincar\u00e9 section. The effects of the control force on chaotic motions have been strongly analyzed, and the control efficiency is found in the cases <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>g<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mtext>\u2009<\/mml:mtext><\/mml:math>(unmodulated case) and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>g<\/mml:mi><mml:mo>\u2260<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math> with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi mathvariant=\"normal\">\u03a9<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>\u03c9<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>\u03a9<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>w<\/mml:mi><mml:mo>\u2260<\/mml:mo><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>; <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>p<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>q<\/mml:mi><\/mml:math> are simple positive integers. Vibrational resonance (VR), hysteresis, and coexistence of several attractors have been studied in detail based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations.<\/jats:p>","DOI":"10.1155\/2020\/8823458","type":"journal-article","created":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T08:48:54Z","timestamp":1602060534000},"page":"1-16","source":"Crossref","is-referenced-by-count":20,"title":["Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos"],"prefix":"10.1155","volume":"2020","author":[{"given":"A. V.","family":"Monwanou","sequence":"first","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. A.","family":"Koukp\u00e9m\u00e8dji","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"},{"name":"D\u00e9partement de Physique, FAST-Natitingou, Universit\u00e9 Nationale des Sciences, Technologies, Ing\u00e9nierie et Math\u00e9matiques, Abomey, Benin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Ainamon","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. R.","family":"Nwagoum Tuwa","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"},{"name":"Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes and TWAS Research Unit, Faculty of Science, University of Yaound\u00e9 I, P. O. 812, Yaound\u00e9, Cameroon"},{"name":"Research Unit of Industrial Systems Engineering and Environment (RU-ISEE), Fosto-Victor University Institute of Technology, University of Dschang, P. O. Box 134, Bandjoun, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9369-9583","authenticated-orcid":true,"given":"C. H.","family":"Miwadinou","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"},{"name":"D\u00e9partement de Physique, ENS-Natitingou, Universit\u00e9 Nationale des Sciences, Technologies, Ing\u00e9nierie et Math\u00e9matiques, Abomey, Benin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. B.","family":"Chabi Orou","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB), Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, Benin"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","year":"2014"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1002\/cae.22070"},{"issue":"15","key":"3","first-page":"870","volume":"4","year":"2015","journal-title":"Chemical Science Review and Letters"},{"key":"4","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1021\/ar030230t","volume":"37","year":"2004","journal-title":"Accounts of Chemical Research"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/s0960-0779(02)00106-6"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/s0020-7462(02)00201-9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1063\/1.4962403"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/33\/45\/103"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.5890\/jand.2015.11.006"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.99.052221"},{"key":"11","first-page":"49","volume":"386387","year":"2019","journal-title":"Physica D"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cjph.2018.03.033"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.09.017"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.05.021"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127418300057"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.66.036219"},{"key":"17","year":"1977"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1021\/cr00035a012"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/0039-6028(81)90165-5"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(86)87099-3"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90239-6"},{"key":"22","year":"1964"},{"key":"23","year":"1981"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8823458.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8823458.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8823458.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T08:48:55Z","timestamp":1602060535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/8823458\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,5]]},"references-count":23,"alternative-id":["8823458","8823458"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8823458","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,5]]}}}