This work is about understanding the dynamics of neuronal systems, in particular with
respect to brain connectivity. It addresses complex neuronal systems by looking at
neuronal interactions and their causal relations. These systems are characterized using
a generic approach to dynamical system analysis of brain signals - dynamic causal
modelling (DCM). DCM is a technique for inferring directed connectivity among
brain regions, which distinguishes between a neuronal and an observation level. DCM
is a natural extension of the convolution models used in the standard analysis of
neuroimaging data. This thesis develops biologically constrained and plausible
models, informed by anatomic and physiological principles. Within this framework, it
uses mathematical formalisms of neural mass, mean-field and ensemble dynamic
causal models as generative models for observed neuronal activity. These models
allow for the evaluation of intrinsic neuronal connections and high-order statistics of
neuronal states, using Bayesian estimation and inference. Critically it employs
Bayesian model selection (BMS) to discover the best among several equally plausible
models. In the first part of this thesis, a two-state DCM for functional magnetic
resonance imaging (fMRI) is described, where each region can model selective
changes in both extrinsic and intrinsic connectivity. The second part is concerned with
how the sigmoid activation function of neural-mass models (NMM) can be
understood in terms of the variance or dispersion of neuronal states. The third part
presents a mean-field model (MFM) for neuronal dynamics as observed with
magneto- and electroencephalographic data (M/EEG). In the final part, the MFM is
used as a generative model in a DCM for M/EEG and compared to the NMM using
Bayesian model selection