Chaotic dynamics, topological analysis and flat analog electronic control by physiological signals of a neurally-inspired system
Résumé
A novel abstract bicompartmental neural model based on a cubic nonlinearity, consisting of introducing a Josephson junction as a coupling element, is presented. Through numerical simulations and experimental measurements involving an analog electronic circuit, it is found that the system can generate a double-scroll chaotic attractor endowed with a remarkably complex topology. This is accompanied by diversification of the spectral signature across its four variables and multistability. An analysis of the global observability and controllability is conducted, leading to the synthesis of a flat controller that can steer the dynamics towards those of structurally different entities, as exemplified by a modified Lorenz system. The first analog realization of flat control is then introduced. The possibility of low-latency and high-accuracy manipulation of the dynamics is demonstrated by considering the challenging case of tracking extraneous external signals, namely, physiological recordings indexing autonomic and central nervous system activity. Besides showing the flexibility and adaptability of the approach, the controller enables the concomitant generation of multiple additional signals with spectrogram features compared to the individual inputs, offering a promising substrate for future applications in physical time series data augmentation.