EFFECT OF A RESONANT PERIODIC PERTURBATION ON NONLINEAR PROCESSES

The effect of a periodic modulation on the bifurcation parameter of the logistic map is investigated. Attention is limited to the case where the modulation parameter A t always lies within the stability range of a P -furcation of the unperturbed logistic map. In particular, we focus our interest in the near resonance behavior, i. e. when the external modulation frequency ω is close to the “natural” logistic oscillator frequency, ω 0 = 1/ P. The study of the Lyapunov exponent shows that, above a critical modulation amplitude, a sharply delimited frequency interval exists around ω 0 in which the external modulation has a resonant effect, inducing a qualitative modification of the dynamics, even when the modulation amplitude is relatively small. It consists in locking the phase of the external perturbation to our nonlinear logistic oscillator.