{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:42:27Z","timestamp":1790876547264,"version":"4.1.0"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"name":"Agencia Estatal de Investigacion of Spain","award":["PID2022-136613NB-100"],"award-info":[{"award-number":["PID2022-136613NB-100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:p>Damped and driven oscillators are generally modeled with a nonautonomous second-order nonlinear ordinary differential equation including a sinusoidal driving forcing term, such as the forced Duffing equation and the forced Holmes\u2013Rand equation. These equations have been extensively studied during the last century and the last two decades. In the early 1990s, Abarbanel, Rabinovich and Sushchik proposed replacing the sinusoidal forcing term with a \u201cforce controlled by the movements of the oscillator itself\u201d, i.e. by the product of two variables: the first being the solution of the oscillator itself, while the second is the solution of a first-order nonlinear ordinary differential equation. They referred to the resulting autonomous dynamical system of two coupled nonlinear ordinary differential equations as a \u201ccontrolled nonlinear oscillator\u201d. To that end, they introduced a change of variables and parameters to transform the \u201ccontrolled nonlinear oscillator\u201d that corresponds to a particular case of the forced Duffing equation into the Lorenz system. The aim of this work is to show that their idea can be further generalized and applied to many other dynamical systems, including the forced Holmes\u2013Rand equation, Chua\u2019s cubic circuit, Chen\u2019s system and the forced Helmholtz oscillator. It is proved that a certain class of three-dimensional dynamical systems can be rewritten into the form of \u201cgeneralized controlled nonlinear oscillators\u201d, which can then be transformed into various Lorenz-like systems. Such a transformation could be very useful for the study of intermittent chaos.<\/jats:p>","DOI":"10.1142\/s0218127426300223","type":"journal-article","created":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T04:12:58Z","timestamp":1777263178000},"source":"Crossref","is-referenced-by-count":3,"title":["From Generalized Controlled Nonlinear Oscillators to Lorenz-Like Systems"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1400-4136","authenticated-orcid":false,"given":"Jean-Marc","family":"Ginoux","sequence":"first","affiliation":[{"name":"CNRS, LIS, Aix Marseille University, Universit\u00e9 de Toulon, Toulon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4547-5758","authenticated-orcid":false,"given":"Riccardo","family":"Meucci","sequence":"additional","affiliation":[{"name":"National Institute of Optics \u2014 CNR, Florence, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-5999","authenticated-orcid":false,"given":"Jaume","family":"Llibre","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1381-7418","authenticated-orcid":false,"given":"Guanrong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1652-5464","authenticated-orcid":false,"given":"Leon O.","family":"Chua","sequence":"additional","affiliation":[{"name":"Department of EECS, University of California, Berkeley, CA 94720, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2026,4,25]]},"reference":[{"key":"S0218127426300223BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/2036"},{"key":"S0218127426300223BIB002","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-20.3.180"},{"key":"S0218127426300223BIB003","doi-asserted-by":"publisher","DOI":"10.2307\/1969181"},{"key":"S0218127426300223BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"S0218127426300223BIB005","unstructured":"Chen, G. 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