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.

Keywords

• adaptive synchronization
• generalized synchronization
• Rössler system
• chaotic circuit
• chaotic system
• nonlinear dynamics