Abstract

Chaotic Dynamics in Parametric Sound Generation

V.Espinosa, V.J.Sanchez-Morcillo, J.Ramis (Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, Grao de Gandia, Spain)

e-mail: vespinos@fis.upv.es

The search for chaotic behaviour has evolved from its association to complex systems with high number of degrees of freedom, to be common in relatively simple systems described by a set of coupled nonlinear evolution equations of few variables. We claim that a phenomenon showing such low-dimensional chaos is the parametric generation of sound in a dispersive cavity. The model was proposed in [L.A. Ostrovsky et al., Acustica 39, 298 (1978)], where it was shown that, above the subharmonic generation threshold, bistable stationary solutions exist for positive values of the product of the fundamental (pump) and subharmonic detunings. We show that for negative values of this product the amplitudes of the fields display self-pulsing behavior and a route to chaos. This regime can be achieved by considering different losses for each frequency in the resonator. The observed behaviour is in close analogy with the dynamics reported for a similar optical system. We believe that the theory presented describes experimental results observed several decades ago [B.D. Cook, J. Opt. Soc. Am. 85, S1 (1989)].

Section : 8