Identifying empirical equations of chaotic circuit from data

Chaotic analog circuits are commonly used to demonstrate the physical existence of chaotic systems and investigate the variety of possible applications. A notable disparity between the analog circuit and the computer model of a chaotic system is usually observed, caused by circuit element imperfectness and numerical errors in discrete simulation. In order to show that the major component of observable error originates from the circuit and to obtain its accurate white-box model, we propose a novel technique for reconstructing ordinary differential equations (ODEs) describing the circuit from data. To perform this task, a special system reconstruction algorithm based on iteratively reweighted least squares and a special synchronization-based technique for comparing model accuracy are developed. We investigate an example of a well-studied Rössler chaotic system. We implement the circuit using two types of operational amplifiers. Then, we reconstruct their ODEs from the recorded data. Finally, we compare original ODEs, SPICE models, and reconstructed equations showing that the reconstructed ODEs have approximately 100 times lower mean synchronization error than the original equations. The proposed identification technique can be applied to an arbitrary nonlinear circuit in order to obtain its accurate empirical model.