Effects of Higher Order and Long-Range Synchronizations for Classification and Computing in Oscillator-Based Spiking Neural Networks

Development of artificial oscillator-based spiking neural networks (SNN), which are able to solve effectively various cybernetics problems including image recognition and adaptive control, is a key line of research. We have thoroughly explored the scheme of two thermally coupled $VO_2$ oscillators and found its effect of high order synchronization (HOS), which may be used to increase SNN classification capacity $N_s$. Phase-locking estimation method has been developed to determine values of subharmonic ratio SHR and synchronization effectiveness {\eta}. The experimental scheme has $N_s=12$ and SHR distributions are shaped as Arnold's tongues. In a model $N_s$ may reach maximum of $N_s>150$ at certain levels of coupling strength and noise. We demonstrate the long-range synchronization effect in a one-dimensional chain of oscillators and the phenomenon of synchronization transfer even at low values of {\eta} for intermediate links. The paper demonstrates realization of analogue operation of "multiplication", binary logic, and possibility of development of the interface between SNN and computer. The described effects increasing classification capacity of oscillator schemes and calculation principles based on the universal physical effect - HOS may be applied for any spiking type oscillators with any coupling type therefore enhancing practical value of the presented results to expand SNN capabilities.