Transient spatiotemporal chaos collapses into periodic and steady states in an electrically-coupled neural ring network

Abstract

Chaotic behavior in a spatially extended system is often referred to as spatiotemporal chaos. The trajectories of a system as it evolves through state space are described by irregular spatial and temporal patterns. In mathematical biology, spatiotemporal chaos has been demonstrated in chemotaxis models (Painter & Hillen, 2011) predator-prey models (Sherratt, J. & Fowler, A., 1995) and the Hogdkin-Huxley neural model (Wang, Lu, & Chen, 2006). Transient chaos is a special case of chaotic dynamics in which the system dynamics collapses without external perturbation. Rather, collapse is an intrinsic property of the system. Here, we diff usively couple many spiking neurons into a ring network and fi nd that the network dynamics can collapse on to two diff erent species of attractor: the limit cycle and the steady-state solution.