Transients, metastability, and neuronal dynamics.

This paper is about neuronal dynamics and how their special complexity can be understood in terms of nonlinear dynamics. There are many aspects of neuronal interactions and connectivity that engender the complexity of brain dynamics. In this paper we consider (i) the nature of this complexity and (ii) how it depends on connections between neuronal systems (e.g., neuronal populations or cortical areas). The main conclusion is that simulated neural systems show complex behaviors, reminiscent of neuronal dynamics, when these extrinsic connections are sparse. The patterns of activity that obtain, under these conditions, show a rich form of intermittency with the recurrent and self-limiting expression of stereotyped transient-like dynamics. Despite the fact that these dynamics conform to a single (complex) attractor this metastability gives the illusion of a dynamically changing attractor manifold (i.e., a changing surface upon which the dynamics unfold). This metastability is characterized using a measure that is based on the entropy of the time series' spectral density.