Peter A. Robinson

TL;DR: It is argued that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

TL;DR: These equations incorporate nonlinearities, axonal and dendritic lags, excitatory and inhibitory neuronal populations, and the two-dimensional nature of the cortex, while rendering nonlinear features far more tractable than previous formulations, both analytically and numerically.

TL;DR: Different variants of the BOLD signal equation are embedded in a well-established DCM of functional interactions among visual areas to compare the ensuing models using Bayesian model selection and demonstrate that the best model is a non-linear model with a revised form for the coefficients, in which ε is treated as a free parameter.

TL;DR: This study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain, and argues that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted and interrelated by the global bifURcation diagram of the model's dynamics.

TL;DR: A nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters and provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.