Europhys. Lett.
Volume 70, Number 1, April 2005
Page(s) 56 - 62
Section General
Published online 04 March 2005
Europhys. Lett., 70 (1), pp. 56-62 (2005)
DOI: 10.1209/epl/i2004-10465-1

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

R. Chacón

Departamento de Electrónica e Ingeniería Electromecánica Escuela de Ingenierías Industriales, Universidad de Extremadura Apartado Postal 382, E-06071, Badajoz, Spain

received 21 April 2004; accepted in final form 7 February 2005
published online 4 March 2005

A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. These equations provide a feedback autoresonance-controlling mechanism. The theory is applied to Duffing-like systems to obtain exact analytical expressions for autoresonance excitations and solutions which explain all the phenomenological and approximate results arising from a previous (adiabatic) approach to autoresonance phenomena in such systems. The theory is also applied to obtain new, general, and exact properties concerning autoresonance phenomena in a broad class of dissipative and Hamiltonian systems, including (as a particular case) Duffing-like systems.

05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.

© EDP Sciences 2005