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A general exact theory of autoresonance (self-sustained resonance) in bothdissipative and Hamiltonian nonautonomous systems is presented. The equationsthat together govern the autoresonance solutions and excitations are derivedwith the aid of a variational principle concerning the power functional. Thetheory is applied to Duffing oscillators to obtain exact analytical expressionsfor autoresonance excitations and solutions which explain all thephenomenological and approximate results arising from the previous approach toautoresonance phenomena.Comment: 12 pages, LaTeX; figures adde

Energy-based theory of autoresonance phenomena: Application to Duffing-like systems