Generation of Chaotic Beats

Abstract

We show that coupled Kerr and Duffing oscillators with small nonlinearities and strong external pumping can generate chaotic and hyperchaotic beats. The appearance of chaos within beats depends strongly on the type of interactions between the nonlinear oscillators. To indicate chaotic behavior of the system we make use of the Lyapunov exponents. The structure of chaotic beats can be qualitatively different — the envelope function can be smooth if the system is undamped or can give the impression of noise structure in the presence of strong damping and nonlinear interactions between the individual oscillators. The systems considered can be used, in practice, as generators of chaotic beats with chaotically modulated envelopes and frequencies.

Generation of Chaotic Beats in a Modified Chua's Circuit Part I: Dynamic Behaviour

“…In recent times, an attractive phenomenon has been investigated in [4], where the behaviors of Kerr and Duffing nonlinear oscillators driven by two sinusoidal inputs with slightly different frequencies have been analyzed. In particular, the authors of reference [4] started by considering that in linear systems the interaction of two sinusoidal signals generates the well-known phenomenon called beats [5].…”

“…In particular, the authors of reference [4] started by considering that in linear systems the interaction of two sinusoidal signals generates the well-known phenomenon called beats [5]. Namely, when two waves with slightly different frequencies interfere, the frequency of the resulting waveform is the average of the frequencies of the two waves, whereas its amplitude is modulated by an envelope, the frequency of which is the difference between the frequencies of the two waves.…”

Chaotic Beats in a Nonautonomous System Governing Second-Harmonic Generation of Light

“…If the system is chaotic, this type of vibrations are referred to as chaotic beats [Grygiel & Szlachetka, 2002]. In the simplest cases chaotic beats can be interpreted as a "signal" with chaotic envelopes and a stable fundamental frequency.…”

Two-time synchronism and induced synchronization in a Kerr coupler

“…The Kerr systems occupy an important position in optical devices and have been extensively investigated in the classical as well as quantum approach (for a review, see Ref. [27,28]). We study Eqs.…”

“…As seen, the beats whose structure resembles the original trace voice [23] have chaotic envelopes and stable fundamental frequencies [3,28]. Let us now consider the synchronization of beats presented in Fig.2, when the feedback terms are switched on at the time t 0 = 480.…”