Synchronous tonic-to-bursting transitions in a neuronal hub motif

Abstract

We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.

Introduction to Focus Issue: Nonlinear science of living systems: From cellular mechanisms to functions

“…Synchronization of neurons in neuronal networks of varying size and of various coupling types is of major importance when trying to gain an understanding of different aspects of brain functions. Follmann et al (2018) investigate a neuronal network with gap junction coupling and demonstrate in numerical simulations how neurons synchronize into different robust states evolving through interesting period-doubling cascades and transitions to chaos.…”

“…These modeling approaches have been extended to examine the impact of nonlinear dynamics and noise in higher functions such as psychiatric disorders and in autonomic processes such as stress and sleep (e.g., Braun et al, 2008). The reader will find the HB model used in this Focus Issue for elucidating multi-stable behavior of neural networks (Orio et al, 2018), evaluating the network effects of neuronal diversity (Tchaptchet, 2018), examining synchronization states during sleep and wakefulness (Holmgren Hopkins et al, 2018), and demonstrating synchronous neuronal transitions (Follmann et al, 2018).…”