{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T09:19:33Z","timestamp":1747732773216,"version":"3.40.5"},"reference-count":69,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,12,15]]},"abstract":"<jats:p>In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.<\/jats:p>","DOI":"10.1142\/s021812742050234x","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T10:44:48Z","timestamp":1607597088000},"page":"2050234","source":"Crossref","is-referenced-by-count":4,"title":["The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9197-8711","authenticated-orcid":false,"given":"L.","family":"Kamdjeu Kengne","sequence":"first","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon"},{"name":"Unit\u00e9 de Recherche de Mati\u00e8re Condens\u00e9e, d\u2019Electronique et de Traitement du Signal (UR-MACETS), Department of Physics, University of Dschang, P. O. Box 67, Dschang, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Z. Tabekoueng","family":"Njitacke","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon"},{"name":"Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P. O. Box 63, Buea, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. R. Mboupda","family":"Pone","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. T. Kamdem","family":"Tagne","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche de M\u00e9canique et de Mod\u00e9lisation des Syst\u00e8mes Physiques (UR-2MSP), Department of Physics, University of Dschang, P. O. Box 67, Dschang, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,12,9]]},"reference":[{"key":"S021812742050234XBIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415500753"},{"key":"S021812742050234XBIB002","doi-asserted-by":"crossref","first-page":"3872573","DOI":"10.1155\/2018\/3872573","volume":"2018","author":"Bao B.","year":"2018","journal-title":"Complexity"},{"key":"S021812742050234XBIB003","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.chaos.2018.02.031","volume":"109","author":"Bao B.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500068"},{"key":"S021812742050234XBIB005","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.chaos.2004.11.005","volume":"25","author":"Bishop S.","year":"2005","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB006","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1016\/S0960-0779(00)00245-9","volume":"12","author":"Cao H.","year":"2001","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB007","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/BF02704570","volume":"64","author":"Dana S.","year":"2005","journal-title":"Pramana"},{"key":"S021812742050234XBIB008","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.aeue.2018.03.035","volume":"90","author":"Fonzin T. F.","year":"2018","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"S021812742050234XBIB009","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1515\/zna-2019-0286","volume":"75","author":"Fozin T. F.","year":"2019","journal-title":"Z. Naturforsch. A"},{"key":"S021812742050234XBIB010","doi-asserted-by":"crossref","first-page":"113105","DOI":"10.1063\/1.5121028","volume":"29","author":"Fonzin Fozin T.","year":"2019","journal-title":"Chaos"},{"key":"S021812742050234XBIB011","doi-asserted-by":"crossref","first-page":"113030","DOI":"10.1088\/1367-2630\/12\/11\/113030","volume":"12","author":"Heinrich M.","year":"2010","journal-title":"New J. Phys."},{"key":"S021812742050234XBIB012","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198507239.001.0001","volume-title":"Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers","author":"Hilborn R. C.","year":"2000"},{"key":"S021812742050234XBIB013","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.physleta.2013.01.009","volume":"377","author":"Jafari S.","year":"2013","journal-title":"Phys. Lett. A"},{"key":"S021812742050234XBIB014","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1142\/S0218127493000805","volume":"3","author":"Kahlert C.","year":"1993","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S021812742050234XBIB015","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1007\/s11071-015-2364-y","volume":"83","author":"Kengne J.","year":"2016","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB016","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s11071-016-3047-z","volume":"87","author":"Kengne J.","year":"2017","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB017","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.cnsns.2017.04.017","volume":"52","author":"Kengne J.","year":"2017","journal-title":"Commun. Nonlin. Sci. Numer. Simul."},{"key":"S021812742050234XBIB018","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.chaos.2019.01.033","volume":"121","author":"Kengne J.","year":"2019","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB019","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1007\/s40435-020-00613-2","volume":"8","author":"Kengne L. K.","year":"2020","journal-title":"Int. J. Dyn. Contr."},{"key":"S021812742050234XBIB020","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s10470-020-01601-4","volume":"103","author":"Kengne L. K.","year":"2020","journal-title":"Anal. Integr. Circuits Sign. Process."},{"key":"S021812742050234XBIB021","doi-asserted-by":"crossref","first-page":"153146","DOI":"10.1016\/j.aeue.2020.153146","volume":"118","author":"Kengne L. K.","year":"2020","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"S021812742050234XBIB022","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1140\/epjp\/s13360-020-00338-3","volume":"135","author":"Kengne L. K.","year":"2020","journal-title":"Eur. Phys. J. Plus"},{"key":"S021812742050234XBIB023","first-page":"2171","volume":"228","author":"Kuate P. D. K.","year":"2019","journal-title":"Eur. Phys. J.: Special Topics"},{"key":"S021812742050234XBIB024","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.cnsns.2017.03.010","volume":"51","author":"Kuznetsov N.","year":"2017","journal-title":"Commun. Nonlin. Sci. Numer. Simul."},{"key":"S021812742050234XBIB025","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416501777"},{"key":"S021812742050234XBIB026","doi-asserted-by":"crossref","first-page":"12","DOI":"10.3390\/e20010012","volume":"20","author":"Lai Q.","year":"2018","journal-title":"Entropy"},{"key":"S021812742050234XBIB027","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.chaos.2018.07.011","volume":"114","author":"Lai Q.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB028","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1109\/TCSII.2019.2927371","volume":"67","author":"Lai Q.","year":"2019","journal-title":"IEEE Trans. Circuits Syst.-II: Expr. Briefs"},{"key":"S021812742050234XBIB029","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1016\/j.physleta.2011.04.037","volume":"375","author":"Leonov G.","year":"2011","journal-title":"Phys. Lett. A"},{"key":"S021812742050234XBIB030","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.chaos.2018.05.017","volume":"113","author":"Leutcho G. D.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB031","doi-asserted-by":"crossref","first-page":"109703","DOI":"10.1016\/j.chaos.2020.109703","volume":"134","author":"Leutcho G. D.","year":"2020","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB032","doi-asserted-by":"crossref","first-page":"033112","DOI":"10.1063\/1.5142777","volume":"30","author":"Leutcho G. D.","year":"2020","journal-title":"Chaos"},{"key":"S021812742050234XBIB033","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1007\/s11071-013-0866-z","volume":"73","author":"Li C.","year":"2013","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB034","doi-asserted-by":"crossref","first-page":"2059","DOI":"10.1007\/s11071-014-1568-x","volume":"78","author":"Li C.","year":"2014","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415300256"},{"key":"S021812742050234XBIB036","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416502333"},{"key":"S021812742050234XBIB037","doi-asserted-by":"crossref","first-page":"120501","DOI":"10.1088\/1674-1056\/26\/12\/120501","volume":"26","author":"Li C.-B.","year":"2017","journal-title":"Chinese Phys. B"},{"key":"S021812742050234XBIB038","doi-asserted-by":"crossref","first-page":"083101","DOI":"10.1063\/1.4997051","volume":"27","author":"Li C.","year":"2017","journal-title":"Chaos"},{"key":"S021812742050234XBIB039","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1007\/s11071-017-3729-1","volume":"90","author":"Li C.","year":"2017","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB040","doi-asserted-by":"crossref","first-page":"026313","DOI":"10.1103\/PhysRevE.80.026313","volume":"80","author":"Lucarini V.","year":"2009","journal-title":"Phys. Rev. E"},{"key":"S021812742050234XBIB041","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1080\/00207721.2017.1410251","volume":"49","author":"Mobayen S.","year":"2018","journal-title":"Int. J. Syst. Sci."},{"key":"S021812742050234XBIB042","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.chaos.2018.01.011","volume":"107","author":"Negou A. N.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB043","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10470-019-01436-8","volume":"101","author":"Negou A. N.","year":"2019","journal-title":"Analog Integr. Circuits Sign. Process."},{"key":"S021812742050234XBIB044","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.chaos.2018.01.004","volume":"107","author":"Njitacke Z.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB045","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126619501214"},{"key":"S021812742050234XBIB046","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s40435-018-0435-x","volume":"7","author":"Njitacke Z.","year":"2019","journal-title":"Int. J. Dyn. Contr."},{"key":"S021812742050234XBIB047","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1007\/s40435-019-00509-w","volume":"7","author":"Njitacke Z.","year":"2019","journal-title":"Int. J. Dyn. Contr."},{"key":"S021812742050234XBIB048","first-page":"1133","volume":"229","author":"Njitacke Z. T.","year":"2020","journal-title":"Eur. Phys. J.: Special Topics"},{"key":"S021812742050234XBIB049","doi-asserted-by":"crossref","first-page":"3424","DOI":"10.1007\/s00034-019-01324-6","volume":"39","author":"Njitacke Z. T.","year":"2020","journal-title":"Circuits Syst. Sign. Process."},{"key":"S021812742050234XBIB050","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/0960-0779(94)00146-H","volume":"5","author":"Okni\u0144ski A.","year":"1995","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB051","doi-asserted-by":"crossref","first-page":"9111","DOI":"10.1016\/j.ijleo.2016.06.111","volume":"127","author":"Pham V.-T.","year":"2016","journal-title":"Optik"},{"key":"S021812742050234XBIB052","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1007\/s11071-016-3170-x","volume":"87","author":"Pham V.-T.","year":"2017","journal-title":"Nonlin. Dyn."},{"key":"S021812742050234XBIB053","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.chaos.2019.02.003","volume":"120","author":"Pham V. T.","year":"2019","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB054","first-page":"1","volume":"103","author":"Pone J. R. M.","year":"2019","journal-title":"Anal. Integr. Circuits Sign. Process."},{"key":"S021812742050234XBIB055","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40435-018-0431-1","volume":"7","author":"Pone J. R. M.","year":"2019","journal-title":"Int. J. Dyn.Contr."},{"key":"S021812742050234XBIB056","doi-asserted-by":"crossref","first-page":"104636","DOI":"10.1016\/j.mejo.2019.104636","volume":"93","author":"Sadecki J.","year":"2019","journal-title":"Microelectron. J."},{"key":"S021812742050234XBIB057","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.chaos.2018.06.008","volume":"113","author":"Signing V. F.","year":"2018","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB058","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/j.chaos.2005.07.014","volume":"28","author":"Sofroniou A.","year":"2006","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050234XBIB059","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414500096"},{"key":"S021812742050234XBIB060","first-page":"1979","volume":"226","author":"Sprott J. C.","year":"2017","journal-title":"Eur. Phys. J.: Special Topics"},{"key":"S021812742050234XBIB061","doi-asserted-by":"crossref","first-page":"023101","DOI":"10.1063\/1.5132280","volume":"30","author":"Tabekoueng Njitacke Z.","year":"2020","journal-title":"Chaos"},{"key":"S021812742050234XBIB062","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10470-020-01591-3","volume":"103","author":"Tapche R. W.","year":"2020","journal-title":"Anal. Integr. Circuits Sign. Process."},{"key":"S021812742050234XBIB063","doi-asserted-by":"crossref","first-page":"3549","DOI":"10.1021\/acs.jpcc.6b10343","volume":"121","author":"Tong W.","year":"2017","journal-title":"J. Phys. Chem. C"},{"key":"S021812742050234XBIB064","first-page":"1575","volume":"224","author":"Vaidyanathan S.","year":"2015","journal-title":"Eur. Phys. J.: Special Topics"},{"key":"S021812742050234XBIB065","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501272"},{"key":"S021812742050234XBIB066","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0167-2789(85)90011-9","volume":"16","author":"Wolf A.","year":"1985","journal-title":"Physica D"},{"key":"S021812742050234XBIB067","doi-asserted-by":"crossref","first-page":"2526","DOI":"10.1016\/j.ijleo.2013.10.123","volume":"125","author":"Xu Y.","year":"2014","journal-title":"Optik"},{"key":"S021812742050234XBIB068","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijnonlinmec.2018.08.012","volume":"106","author":"Zhang S.","year":"2018","journal-title":"Int. J. Non-Lin. Mech."},{"key":"S021812742050234XBIB069","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1002\/cta.2339","volume":"46","author":"Zhou L.","year":"2018","journal-title":"Int. J. Circuit Th. Appl."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812742050234X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,18]],"date-time":"2024-08-18T20:54:12Z","timestamp":1724014452000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812742050234X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,9]]},"references-count":69,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2020,12,15]]}},"alternative-id":["10.1142\/S021812742050234X"],"URL":"https:\/\/doi.org\/10.1142\/s021812742050234x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2020,12,9]]}}}