Chaos in Homeostatically Regulated Neural Systems

TL;DR

This paper shows that homeostatic regulation in neural networks can paradoxically produce complex low-dimensional dynamics like chaos and oscillations, explaining phenomena observed in the brain.

Contribution

It introduces a mechanism by which homeostatic regulation leads to rich neural dynamics, supported by analytical and numerical analysis of Wilson-Cowan networks.

Findings

Homeostatic regulation can induce chaos and oscillations in neural networks.

Rich dynamics are preserved under various network configurations.

Single node behavior determines network dynamics through synchronization.

Abstract

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 a type of 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. This is true for 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.