Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model

Linear instabilities are analyzed in a physiologically based mean-field corticothalamic model and a reduced-parameter model derived from it. In both models, the stable zone corresponding to normal arousal states is bounded by a series of surfaces demarcating the onsets of instabilities. The stable zone is found to depend on delay and rate parameters, whose values have a simple relationship to the number of instabilities and dominant frequencies on the stable zone's boundary. The dominant frequencies of linear activity inside the stable zone are found to lie in clearly delineated regions, each corresponding to an instability surface on its boundary and having approximately the same dominant frequency. These regions are ordered in parameter space according to their dominant frequencies, and an instability associated with the intrathalamic loop is shown to have the highest frequency that can become unstable. This reveals an important role for the thalamus in controlling the stability and bandwidth of dynamics in the corticothalamic system as a whole. The reduced model is found to agree well with the full model in a wide region of parameter space and, thus, is a useful guide to the full model's dynamics.