Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

OBSERVATION OF CHAOTIC BEATS IN A DRIVEN MEMRISTIVE CHUA'S CIRCUIT

In this paper, a time varying resistive circuit realizing the action of an active three segment piecewise linear flux controlled memristor is proposed. Using this as the nonlinearity, a driven Chua's circuit is implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less conductive OFF state and a more conductive ON state. This chaotic switching is governed by the dynamics of the driven Chua's circuit of which the memristor is an integral part. The occurrence of beats is essentially due to the interaction of the memristor aided self-oscillations of the circuit and the external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor switching and that of the external force, constructive and destructive interferences occur leading to revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical simulations and Multisim modeling as well as statistical analyses have been carried out to observe as well as to understand and verify the mechanism leading to chaotic beats.

GENERATION OF STRONGLY CHAOTIC BEATS

This letter proposes a procedure for generating strongly chaotic beats that have been hardly obtainable hitherto. The beats are produced in a nonlinear optical system governing second-harmonic generation of light. The proposition is based on the concept of an optical coupler, but can be easily adopted to other nonlinear systems and Chua's circuits.

CHAOTIC BEATS IN A NONAUTONOMOUS SYSTEM GOVERNING SECOND-HARMONIC GENERATION OF LIGHT

This letter proposes a procedure for generation and control of chaotic beats in a dynamical system that is initially in the periodic state. The dynamical system describes a simple nonlinear optical process — second-harmonic generation of light. The periodic states of the system are found to be in analytical forms. We also investigate some aspects of synchronization of chaotic beats in two systems, detuned in the pump fields.

ON THE GENERATION OF CHAOTIC BEATS IN SIMPLE NONAUTONOMOUS CIRCUITS

In this Letter, attention is focused on the dynamics of a second-order nonlinear circuit driven by two sinusoidal signals. The early results reported herein show that the application of signals with slightly different frequencies enables the phenomenon of chaotic beats to be generated. In particular, the beats dynamics are analyzed both in time-domain and state-space, confirming the chaotic behavior of the proposed circuit.

CHAOTIC BEATS IN A MODIFIED CHUA'S CIRCUIT: DYNAMIC BEHAVIOR AND CIRCUIT DESIGN

This paper illustrates the recent phenomenon of chaotic beats in a modified version of Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In order to satisfy the constraints imposed by the beats dynamics, a novel implementation of the voltage-controlled characteristic of the Chua diode is proposed. By using Pspice simulator, the behavior of the designed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the approach.

A NEW PHENOMENON IN NONAUTONOMOUS CHUA'S CIRCUITS: GENERATION OF CHAOTIC BEATS

This paper focuses on the dynamics of coupled Chua's circuits driven by two sinusoidal signals. In particular, it is shown that the application of signals with slightly different frequencies enables the new phenomenon of chaotic beats to be generated. Finally, the application of signals with equal frequencies is discussed, with the aim of understanding the formation of beats in nonlinear circuits.