Chaos in homeostatically regulated neural systems

Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics remains elusive. Here, we consider Wilson-Cowan networks and demonstrate through numerical and analytical work that homeostatic regulation of the network firing rates can paradoxically lead to a rich dynamical repertoire. The dynamics include mixed-mode oscillations, mixed-mode chaos, and chaotic synchronization when the homeostatic plasticity operates on a moderately slower time scale than the firing rates. This is true for a single recurrently coupled node, pairs of reciprocally coupled nodes without self-coupling, and networks coupled through experimentally determined weights derived from functional magnetic resonance imaging data. In all cases, the stability of the homeostatic set point is analytically determined or approximated. The dynamics at the network level are directly determined by the behavior of a single node system through synchronization in both oscillatory and non-oscillatory states. Our results demonstrate that rich dynamics can be preserved under homeostatic regulation or even be caused by homeostatic regulation. When recordings from the brain are analyzed, rich dynamics such as oscillations or low-dimensional chaos are often present. However, a general mechanism for how these dynamics emerge remains unresolved. Here, we explore the potential that these dynamics are caused by an interaction between synaptic homeostasis, and the connectivity between distinct populations of neurons. Using both analytical and numerical approaches, we analyze how data derived connection weights interact with inhibitory synaptic homeostasis to create rich dynamics such chaos and oscillations operating on multiple time scales. We demonstrate that these rich dynamical states are present in simple systems such as single population of neurons with recurrent coupling. The dynamics of these simple systems are directly inherited in large networks while properties of the coupling matrices determine when these rich dynamics emerge as a function of the parameters of the neuronal populations. Indeed, we find that the removal of single nodes or connections can substantially alter where these rich dynamics onset in the parameter space