Adaptive Generalized Synchronization between Circuit and Computer Implementations of the Rössler System

Abstract

The synchronization between chaotic systems implemented in similar ways—e.g., computer models or circuits—is a well-investigated topic. Nevertheless, in many practical applications, such as communication, identification, machine sensing, etc., synchronization between chaotic systems of different implementation types—e.g., between an analog circuit and computer model—might produce fruitful results. In this research, we study the synchronization between a circuit modeling the Rössler chaotic system and a computer model using the same system. The theoretical possibility of this kind of synchronization is proved, and experimental evidence of this phenomenon is given with special attention paid to the numerical methods for computer model simulation. We show that synchronization between a circuit with uncertain parameters and a computer model is possible, and the parameters obtained from the synchronized computer model are in high correspondence with the circuit element specification. The obtained results establish the possibility of using adaptive generalized synchronization for the parameter identification of real systems. It was also found that Heun’s method yielded the most accurate results in synchronization among second-order numerical integration methods. The best among the first-order methods appears to be the Euler–Cromer method, which can be of interest in embedded applications.

Integrate-and-Differentiate Approach to Nonlinear System Identification

“…Special attention is paid to them in applications of nonlinear science. For instance, electronic chaotic system design and investigation require high-precision modeling, for which parameter identification can be performed [38,39]. Digital chaotic systems are often used for data encryption, and system identification can be used for a cryptographic attack against a chaotic encryption method [40].…”

Complete Synchronization and Partial Anti-Synchronization of Complex Lü Chaotic Systems by the UDE-Based Control Method

“…[15][16][17]). In recent years, scholars proposed various control methods to achieve the complete synchronization and partial anti-synchronization of chaotic systems, such as passive control [18], adaptive control [19], sliding mode control [20] and fuzzy control [21]. For complete synchronization, most studies only dealt with chaotic systems containing one-dimensional model uncertainty and external disturbance in the system; in fact, the uncertainty and disturbance of such systems are often multidimensional in number [22][23][24][25][26].…”

Master-slave synchronization in the Rayleigh and Duffing oscillators via elastic and dissipative couplings

“…A. Karimov et. al [21] have studied the adaptive generalized synchronization between an analog circuit and a computer model by comparing the numerical methods used on the computer simulation of chaotic systems. and difficult to predict the behavior.…”