Sincronização de um oscilador eletrônico caótico com uma superposição de sinais de osciladores idênticos

Abstract

An experimental and numerical study of chaos synchronization was carried out between multiple nonlinear oscillators driving a receiving nonlinear oscillator. The main result this study was obtained through unidirectional additive coupling. In this condition the drivers do not interact with each other and do not receive any signal from the receiving oscillator. Thus, we ensure that the drive signals are passed only to the receiver. In describing the steps that led to these observations, we initially presented some fundamental concepts of synchronization between chaotic oscillators and reported some of our initial investigations in which we reproduced results from the literature, which demonstrate some types of synchronism, for example, complete synchronization, delayed synchronization, etc. We present a particular non-linear system, the Gauthier-Bienfang (G-B) system, which we use most frequently in this work. We build G-B type oscillators, characterize their dynamics and perform couplings between two oscillators, in the drive-receiver configuration. Using such a configuration we were able to observe complete and intermittent synchronization. Through the statistical analysis of the events of desynchronization we verify the existence of extreme events of the Dragon-King type. The reproduction of these results from the literature demonstrates that the chaotic oscillators that we built for this work present the expected functioning, giving us confidence to proceed with original investigations. Through numerical calculations and experimental realization of the coupling configuration with more than one director oscillator coupled to the receiving oscillator, we show that a chaotic oscillator synchronizes with a signal that is a linear combination of signals with partial information of the director oscillators. In addition, we demonstrate analytically the convergence of the synchronism of a G-B oscillator to the sum signal when we increase the number of drivers, with ever lower coupling levels. We also investigated this behavior with another nonlinear system, the Lorenz system. Numerically we show the convergence of the trajectory of a Lorenz receiver oscillator to the trajectory of the linear combination of the drivers. The quality of this synchronization has also been shown to increase with the increase in the number of coupled oscillators, for each coupling level. These results, in which a non-linear oscillator synchronizes with a sum signal, open perspectives for investigations of complex coupled network systems.