Recent years have seen a general resurgence of interest in analog signal processing and computing architectures. In addition, extensive theoretical and experimental literature on chaos and analog chaotic oscillators exists. One peculiarity of these circuits is the ability to generate, despite their structural simplicity, complex spatiotemporal patterns when several of them are brought towards synchronization via coupling mechanisms. While by no means a systematic survey, this paper provides a personal perspective on this area. After briefly covering design aspects and the synchronization phenomena that can arise, a selection of results exemplifying potential applications is presented, including in robot control, distributed sensing, reservoir computing, and data augmentation. Despite their interesting properties, the industrial applications of these circuits remain largely to be realized, seemingly due to a variety of technical and organizational factors including a paucity of design and optimization techniques. Some reflections are given regarding this situation, the potential relevance to discontinuous innovation in analog circuit design of chaotic oscillators taken both individually and as synchronized networks, and the factors holding back the transition to higher levels of technology readiness.

In this paper, the problem on secure communication based on chaos synchronization is investigated. The dual channel information transmitting technology is proposed to increase the security of secure communication system. Based on chaos synchronization, a new digital secure communication scheme is presented for a class of master-slave systems. Finally some numerical simulation examples are given to demonstrate the effectiveness of the given results.

This paper presents a novel approach for robust impulsive synchronization of uncertain complex dynamical networks, each node of which possesses chaotic dynamics with different parameters perturbation and external disturbances as well as unknown but bounded network coupling effects. A new sufficient condition is proposed that guarantees the global robust synchronizing of such a network. Finally, the effectiveness of the proposed approach is evaluated by performing simulations on two illustrative examples.

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

In this paper the attention is focused on the numerical study of hyperchaotic 2D-scroll attractors via the Adomian decomposition method. The approach, which provides series solutions of the system equations, is first applied to weakly-coupled Chua's circuits with Hermite interpolating polynomials. Then the method is successfully utilized for achieving hyperchaos synchronization of two coupled Chua's circuits. The reported examples show that the approach presents two main features, i.e., the system nonlinearity is preserved and the chaotic solution is provided in a closed form.

This paper presents a fuzzy model-based approach for synchronization of time-delay chaotic system with input saturation. Time-delay chaotic drive and response system is respectively represented by Takagi-Sugeno (T-S) fuzzy model. Specially, the response system contains input saturation. Using the unidirectional linear error feedback and the parallel distributed compensation (PDC) scheme, we design fuzzy chaotic synchronization system and analyze local stability for synchronization error dynamics. Since time-delay in the transmission channel always exists, we also take it into consideration. The sufficient condition for the local stability of the fuzzy synchronization system with input saturation and channel time-delay is derived by applying Lyapunov-Krasovskii theory and solving linear matrix inequalities (LMI's) problem. Numerical examples are given to demonstrate the validity of the proposed approach.

In this paper, four coupled chaotic circuits generating four-phase quasi-synchronization of chaos are proposed. By tuning the coupling parameter, chaotic wandering over the phase states characterized by the four-phase synchronization occurs. In order to analyze chaotic wandering, dependent variables corresponding to phases of solutions in subcircuits are introduced. Combining the variables with hysteresis decision of the phase states enables statistical analysis of chaotic wandering.

In this study, synchronization phenomena in chaotic oscillators coupled by a transmission line are investigated. In particular investigation using real circuits is done for the first time. It is confirmed that the chaotic subsystems synchronize, although signals propagating along the transmission line are affected by the time delay. Further the period-doubling bifurcation with varying the time delay and anti-phase synchronization phenomena are observed in our circuit model. Also the voltage distribution of transmission line is simulated in order to investigate whether the current flowing through the transmission line is constant or not. It is found that the subsystems synchronize although the current through the transmission line keeps on varying.

In this paper, a novel chaos circuit with long working-life is proposed. The proposed circuit consists of NMOS-coupled discrete-time chaotic cell circuits. By employing chaos synchronization phenomenon, the proposed circuit can achieve long working-life. Since the proposed circuit is less susceptible to breakdown, the rate of the acceptable product for chaos IC can be improved. Furthermore, thanks to the coupling by using NMOSFET's, the loss of the connection line between chaotic cell circuits can be controlled electronically. Therefore, the proposed system designed by using switched-current (SI) techniques is useful as an experimental tool to analyze chaos synchronization phenomena. The validity of the proposed circuits is confirmed by computer simulations and experiments.

In this study, a simple chaos communication system including modulation-demodulation circuits is studied. The influence of modulation-demodulation circuits to chaos synchronization is investigated. For the estimation of communication quality, bit error rate (BER) is calculated by computer simulation when a sequential random pulse information signal is transmitted via this proposed system.

In this paper, the performance of some communication systems using chaos synchronization is evaluated and compared. A new channel model taking the attenuation, impedance mismatch and noise into account, is proposed for the performance evaluation. The evaluation of bit error rate is done for both ideal and non-ideal conditions using the channel model. It is confirmed that some chaos-based communication systems have a good performance compared with conventional analog communication schemes.

In this paper, we investigate bifurcation phenomena ovserved from two autonomous three-dimensional chaotic circuits coupled by an inductor. Two types of synchronization modes are ovserved in this coupled system, i.e., in-phase synchronization and anti-phase synchronization. For the purpose of detailed analysis, we consider the case that the diodes in the subcircuits are assumed to operate as ideal switches. In this case Poincare map is derived as a three-dimensional map, and Lyapunov exponents can be calculated by using exact solutions. Various bifurcation phenomena related with chaos synchronization are clarified. We confirm that various bifurcation phenomena are observed from circuit experiments.

In this paper, we demonstrate how Yamakawa's chaotic chips and Chua's circuits can be used to implement a secure communication system. Furthermore, their performance for the secure communication is discussed.

In this paper, chaos synchronization in coupled discrete-time dynamical systems is studied. Computer results display the interesting synchronization behaviors in the mutually coupled systems. As possible applications of chaos synchronization, parameter estimations and secure communications are proposed. Furthermore, a modified OGY method is given, which converts a chaotic motion into a periodic motion.