We propose a method for the recovery of coupling architecture and the parameters of elements in networks consisting of coupled oscillators described by delay-differential equations. For each oscillator in the network, we introduce an objective function characterizing the distance between the points of the reconstructed nonlinear function. The proposed method is based on the minimization of this objective function and the separation of the recovered coupling coefficients into significant and insignificant coefficients. The efficiency of the method is shown for chaotic time series generated by model equations of diffusively coupled time-delay systems and for experimental chaotic time series gained from coupled electronic oscillators with time-delayed feedback.

Sensory information processing and higher cognitive functions rely on the interactions between thalamus and cortex. Many types of neurological and psychiatric disorders are accompanied or driven by alterations in the brain connectivity. In this study, putative changes in functional and effective corticocortical (CC), thalamocortical (TC), and corticothalamic (CT) connectivity during wakefulness and slow-wave sleep (SWS) in a model of thalamocortical dysrhythmia, TRIP8b ^−/− mice, and in control (wild-type or WT) mice are described. Coherence and nonlinear Granger causality (GC) were calculated for twenty 10 s length epochs of SWS and active wakefulness (AW) of each animal. Coherence was reduced between 4 and ca 20 Hz in the cortex and between cortex and thalamus during SWS compared with AW in WT but not in TRIP8b ^−/− mice. Moreover, TRIP8b ^−/− mice showed lower CT coherence during AW compared with WT mice; these differences were no longer present during SWS. Unconditional GC analysis also showed sleep-related reductions in TC and CT couplings in WT mice, while TRIP8b ^−/− mice showed diminished wake and enhanced sleep CC coupling and rather strong CT-directed coupling during wake and sleep, although smaller during sleep. Conditional GC coupling analysis confirmed the diminished CC and enhanced CT coupling in TRIP8b ^−/− mice. Our findings indicate that altered properties of hyperpolarization-activated cyclic nucleotide-gated cation channels, characterizing TRIP8b ^−/− mice, have clear effects on CC, TC, and CT networks. A more complete understanding of the function of the altered communication within these networks awaits detailed phenotyping of TRIP8b ^−/− mice aimed at specifics of sensory and attentional processes.

A mesoscale network model is proposed for the development of spike and wave discharges (SWDs) in the cortico-thalamo-cortical (C-T-C) circuit. It is based on experimental findings in two genetic models of childhood absence epilepsy–rats of WAG/Rij and GAERS strains. The model is organized hierarchically into two levels (brain structures and individual neurons) and composed of compartments for representation of somatosensory cortex, reticular and ventroposteriomedial thalamic nuclei. The cortex and the two thalamic compartments contain excitatory and inhibitory connections between four populations of neurons. Two connected subnetworks both including relevant parts of a C-T-C network responsible for SWD generation are modelled: a smaller subnetwork for the focal area in which the SWD generation can take place, and a larger subnetwork for surrounding areas which can be only passively involved into SWDs, but which is mostly responsible for normal brain activity. This assumption allows modeling of both normal and SWD activity as a dynamical system (no noise is necessary), providing reproducibility of results and allowing future analysis by means of theory of dynamical system theories. The model is able to reproduce most time-frequency changes in EEG activity accompanying the transition from normal to epileptiform activity and back. Three different mechanisms of SWD initiation reported previously in experimental studies were successfully reproduced in the model. The model incorporates also a separate mechanism for the maintenance of SWDs based on coupling analysis from experimental data. Finally, the model reproduces the possibility to stop ongoing SWDs with high frequency electrical stimulation, as described in the literature.