Phase-locking intermittency induced by dynamical heterogeneity in networks of thermosensitive neurons

In this work, we study the phase synchronization of a neural network and explore how the heterogeneity in the neurons' dynamics can lead their phases to intermittently phase-lock and unlock. The neurons are connected through chemical excitatory connections in a sparse random topology, feel no noise or external inputs, and have identical parameters except for different in-degrees. They follow a modification of the Hodgkin-Huxley model, which adds details like temperature dependence, and can burst either periodically or chaotically when uncoupled. Coupling makes them chaotic in all cases but each individual mode leads to different transitions to phase synchronization in the networks due to increasing synaptic strength. In almost all cases, neurons' inter-burst intervals differ among themselves, which indicates their dynamical heterogeneity and leads to their intermittent phase-locking. We argue then that this behavior occurs here because of their chaotic dynamics and their differing initial conditions. We also investigate how this intermittency affects the formation of clusters of neurons in the network and show that the clusters' compositions change at a rate following the degree of intermittency. Finally, we discuss how these results relate to studies in the neuroscience literature, especially regarding metastability.