Neuron configuration enhances the synchronization dynamics in ring networks with heterogeneous firing patterns

Neuron synchronization is fundamental for brain dynamics. While several efforts have been made to understand neuron coupling between tonic and bursting neurons, the position of neurons in a neural network and its relationship with synchronization is not fully understood. This work investigates the impact of neuronal heterogeneity on firing pattern transitions and synchronization in networks comprising tonic and bursting neurons. Using the Huber-Braun model, we explore two configurations: one with neurons grouped closely and another with maximal separation. Our findings reveal that while increased coupling strength generally promotes synchronization, the specific mix of neuron types and their spatial configuration crucially modulate both synchronization and firing pattern transitions, leading to phenomena such as cluster synchronization and global phase synchrony. The results indicate that the configuration with maximal separation and with mostly bursting neurons synchronizes more quickly. Firing pattern transitions are also configuration-dependent. For example, in the network with half tonic and half bursting, the configuration grouped closely undergoes diverse complex dynamics transition in the synchronized state, while the other configuration synchronize with chaotic bursting dynamics. Behaviors like cluster synchronization are observed in this network. The study underscores the significance of considering neuronal heterogeneity in understanding network dynamics.