Neural Synchronization, Chimera States and Sleep Asymmetry.

We model the dynamics of sleep states in two connected model brain hemispheres, using groups of coupled individual Hindmarsh-Rose neural oscillators. In a single isloated hemisphere, sleep-promoting neurons and wake-promoting neurons exhibit alternating levels of within-group mean field activity, as well as alternating levels of stochastic phase synchronization, as the system moves between simulated day and night. In a two-hemisphere model, we find differences in the behavior of the sleep-promototing or wake-promoting regions between hemispheres, indicative of chimera-like behavior. We observe phase-cluster states, in which different hemispheres exhibit different bursting dynamics, as well as differences in synchronization between hemispheres. This provides a basis for modeling unihemispheric sleep, which occurs naturally in cetaceans and some bird species, among others, as well as asymmetric sleep, which occurs in human subjects suffering from sleep apnea or experiencing the "first night effect" induced by sleeping in a novel environment.

Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons.

Chimera states occur when identically coupled groups of nonlinear oscillators exhibit radically different dynamics, with one group exhibiting synchronized oscillations and the other desynchronized behavior. This dynamical phenomenon has recently been studied in computational models and demonstrated experimentally in mechanical, optical, and chemical systems. The theoretical basis of these states is currently under active investigation. Chimera behavior is of particular relevance in the context of neural synchronization, given the phenomenon of unihemispheric sleep and the recent observation of asymmetric sleep in human patients with sleep apnea. The similarity of neural chimera states to neural "bump" states, which have been suggested as a model for working memory and visual orientation tuning in the cortex, adds to their interest as objects of study. Chimera states have been demonstrated in the FitzHugh-Nagumo model of excitable cells and in the Hindmarsh-Rose neural model. Here, we demonstrate chimera states and chimera-like behaviors in a Hodgkin-Huxley-type model of thermally sensitive neurons both in a system with Abrams-Strogatz (mean field) coupling and in a system with Kuramoto (distance-dependent) coupling. We map the regions of parameter space for which chimera behavior occurs in each of the two coupling schemes.