How do our brains maintain stable thoughts or memories? This research investigates the existence and stability of localized neuronal activity patterns, or "bumps," in networks of spiking neurons. The study explores how these bumps, proposed mechanisms for visual orientation tuning, spatial navigation, and working memory, can persist in a spiking network if neurons fire asynchronously within the bump. The authors demonstrate that a bump solution can exist under specific conditions and show that, within a parameter regime, the bump solution exhibits bistability with an all-off state, triggered by a transient excitatory stimulus. The study details how the activity profile of the spiking network mirrors that of a corresponding population rate model. Furthermore, the paper explores how the bump can lose stability through partial synchronization, leading to either a traveling wave or a return to the all-off state, potentially induced by rapid synaptic timescales or transient excitatory pulses. This research sheds light on the dynamic mechanisms underlying neural stability and activity patterns, with implications for understanding neurological processes. The ability to activate and deactivate bumps with excitatory inputs offers a foundation for future research into physiological relevance and potential therapeutic interventions.
Published in Neural Computation, this research is highly relevant to the journal’s focus on theoretical and computational neuroscience. The study’s exploration of spiking neuron networks and the dynamics of neuronal activity patterns aligns with the journal’s emphasis on mathematical and computational models of neural systems. The work contributes to the understanding of neural coding and information processing in the brain.