Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing.
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.
Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain.
Jesús
J
Casado-Pascual
Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain.
David
D
Cubero
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Ferruccio
F
Renzoni