Experimental evidence for vibrational resonance and enhanced signal transmission in Chua's circuit

We consider a single Chua's circuit and a system of a unidirectionally coupled n-Chua's circuits driven by a biharmonic signal with two widely different frequencies \omega and \Omega, where \Omega >> \omega. We show experimental evidence for vibrational resonance in the single Chua's circuit and undamped signal propagation of a low-frequency signal in the system of n-coupled Chua's circuits where only the first circuit is driven by the biharmonic signal. In the single circuit, we illustrate the mechanism of vibrational resonance and the influence of the biharmonic signal parameters on the resonance. In the n(= 75)-coupled Chua's circuits enhanced propagation of low-frequency signal is found to occur for a wide range of values of the amplitude of the high-frequency input signal and coupling parameter. The response amplitude of the ith circuit increases with i and attains a saturation. Moreover, the unidirectional coupling is found to act as a low-pass filter.Comment: 15 pages, 12 figures, Accepted for Publication in International Journal of Bifurcation and Chao

Synchronizing noisy nonidentical oscillators by transient uncoupling

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them -- a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling

Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

Synchronization Phenomena in Coupled Birkhoff-Shaw Chaotic Systems Using Nonlinear Controllers

In this chapter, the well-known non-autonomous chaotic system, the Birkhoff-Shaw, which exhibits the structure of beaks and wings, typically observed in chaotic neuronal models, is used in a coupling scheme. The Birkhoff-Shaw system is a second-order non-autonomous dynamical system with rich dynamical behaviour, which has not been sufficiently studied. Furthermore, the master-slave (unidirectional) coupling scheme, which is used, is designed by using the nonlinear controllers to target synchronization states, such as complete synchronization and antisynchronization, with amplification or attenuation in chaotic oscillators. It is the first time that the specific method has been used in coupled non-autonomous chaotic systems. The stability of synchronization is ensured by using Lyapunov function stability theorem in the unidirectional mode of coupling. The simulation results from system’s numerical integration confirm the appearance of complete synchronization and antisynchronization phenomena depending on the signs of the parameters of the error functions. Electronic circuitry that models the coupling scheme is also reported to verify its feasibility

Breaking projective chaos synchronization secure communication using filtering and generalized synchronization

This paper describes the security weaknesses of a recently proposed secure communication method based on chaotic masking using projective synchronization of two chaotic systems. We show that the system is insecure and how to break it in two different ways, by high-pass filtering and by generalized synchronization.Comment: 14 pages, 6 figures, latex forma

Chaotic motions in the real fuzzy electronic circuits

Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions, and unpredictability. Consequently, generating chaotic signals on electronic circuit to produce real electrical signals applied to secure communications is an exceedingly important issue. However, nonlinear systems are always composed of many complex equations and are hard to realize on electronic circuits. Takagi-Sugeno (T-S) fuzzy model is a powerful tool, which is described by fuzzy IF-THEN rules to express the local dynamics of each fuzzy rule by a linear system model. Accordingly, in this paper, we produce the chaotic signals via electronic circuits through T-S fuzzy model and the numerical simulation results provided by MATLAB are also proposed for comparison. T-S fuzzy chaotic Lorenz and Chen-Lee systems are used for examples and are given to demonstrate the effectiveness of the proposed electronic circuit. © 2013 Shih-Yu Li et al