{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T09:41:17Z","timestamp":1698313277811},"reference-count":31,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":4851,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Electrical oscillators are called single\u2010controlled when their non\u2010linear elements depend on a unique variable, while they are termed adiabatic when their transient operation signal can be represented as a narrowband\u2010modulated Fourier series with only a finite number of dominant components, including the DC one. the novel method presented here allows one to analyse the dominant dynamics, steady state and dynamical stability of such oscillators. the approach devised is perturbative and is termed averaging, since it moves from the differential equation in the oscillator signal to provide a set of simultaneous differential equations in the complex envelopes of the dominant components of that variable. Owing to the treatment generality, investigable circuit topologies comprise a linear lumped time\u2010invariant network of any order with bias sources, and any number of non\u2010linear elements, with or without memory, with a common control variable. to illustrate the use of the method, formulae concerning a seventh\u2010order oscillator are derived.<\/jats:p>","DOI":"10.1002\/cta.4490210502","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T09:29:02Z","timestamp":1183368542000},"page":"425-436","source":"Crossref","is-referenced-by-count":3,"title":["The averaging perturbation method for the dominant behaviour analysis of adiabatic single\u2010controlled oscillators"],"prefix":"10.1002","volume":"21","author":[{"given":"Antonino M.","family":"Sommariva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Introduction to Non\u2010linear Mechanics","author":"Kryloff N.","year":"1947"},{"key":"e_1_2_1_3_2","volume-title":"Asymptotic Methods in the Theory of Nonlinear Oscillations","author":"Bogoliubov N. 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