Patterns and symmetries in spiking neural networks
Victoria Zhang · Cambridge journal for junior scientists. · 2024
Inspired by recent progress in computational neuroscience and artificial intelligence, this paper explores rich temporal patterns in networks of neurons that communicate via electric pulses known as spikes.In particular, we describe the attractors in small circuits of spiking neurons with different symmetries and connectivities.Using methods developed in the theory of dynamical systems, we extend an analytical approach to capture the phase-locked states and their stability for a general N -cell system.We then systematically explore attractors in reduced state spaces via Poincaré maps for both all-to-all coupled and star-like coupled networks.We identify a sequence of bifurcations when the coupling strengths vary from inhibition to excitation.Moreover, using high-precision numerical simulations, we find two novel states in star-like networks that are unobserved in all-to-all networks: the death of oscillation for inhibitory coupling and quasi-periodic behaviors for excitatory coupling.Our results elucidate the interplay between dynamical patterns and symmetries in the building blocks of real networks.Furthermore, as self-sustained oscillations with pulsatile couplings are ubiquitous, our analysis may clarify understanding of not only neural dynamics but also other pulse-coupled oscillator systems such as non-linear electric circuits, wireless sensor networks, and self-organizing chemical reactions.