Partial synchronization patterns in brain networks

Partial synchronization patterns play an important role in the functioning of neuronal networks, both in pathological and in healthy states. They include chimera states, which consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics, and other complex patterns. In this perspective article we show that partial synchronization scenarios are governed by a delicate interplay of local dynamics and network topology. Our focus is in particular on applications of brain dynamics like unihemispheric sleep and epileptic seizure.

A new scheme of coupling and synchronizing low-dimensional dynamical systems

A different manner of study synchronization between chaotic systems is presented. This is done by using two different forced coupled nonlinear circuits. The way of coupling the systems under study is different from those used in the analysis of chaos in dynamical systems of low dimensionality. The study of synchronization and how to manipulate it, is carried out through the variation of the couplings by calculating the bifurcation diagrams. We observed that for rather larger values of the coupling between the circuits it is reached total synchronization, while for small values of the coupling it is obtained, in the best of the cases, partial synchronization.

Induced seismicity in coal and iron ore regions of Kuzbass

According to the results of seismicity monitoring in the Kemerovo region, seismic activations are studied near coal enterprises and iron ore mines. The spatial-temporal variability of induced seismicity in Kuzbass is shown. It has been established that the strongest subsoil activations in the area of mining occur as short-term activations lasting 1-2 months and repeated several times in one to two years. The following similar activations are already taking place at other objects. Induced seismicity in Mountains Shoria is considered. The effect of partial synchronization of the development of seismicity was discovered at the mines of Kazsky, Sheregeshsky, Tashtagolsky, located one hundred kilometers apart.

Model decomposition of timed event graphs under periodic partial synchronization: application to output reference control

Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1,t2 can only fire if both transitions are simultaneously enabled, PS of transition t1 by transition t2 means that t1 can fire only when transition t2 fires, but t1 does not influence the firing of t2. This, for example can describe the synchronization between a local train and a long distance train. Of course it is reasonable to synchronize the departure of a local train by the arrival of long distance train in order to guarantee a smooth connection for passengers. In contrast, the long distance train should not be delayed due to the late arrival of a local train. Under the assumption that PS is periodic, we can show that the dynamic behavior of a TEG under PS can be decomposed into a time-variant and a time-invariant part. It is shown that the time-variant part is invertible and that the time-invariant part can be modeled by a matrix with entries in the dioid ${\mathcal{M}}_{in}^{ax}\left [\!\left [\gamma ,\delta \right ]\!\right ]$ M i n a x γ , δ , i.e. the time-invariant part can be interpreted as a standard TEG. Therefore, the tools introduced for standard TEGs can be used to analyze and to control the overall system. In particular, in this paper output reference control for TEGs under PS is addressed. This control strategy determines the optimal input for a predefined reference output. In this case optimality is in the sense of the ”just-in-time” criterion, i.e., the input events are chosen as late as possible under the constraint that the output events do not occur later than required by the reference output.

Delay Partial Synchronization of Mutual Delay Coupled Boolean Networks

This paper studies the delay partial synchronization for mutual delay-coupled Boolean networks. First, the mutual delay-coupled Boolean network model is presented. Second, some necessary and sufficient conditions are derived to ensure the delay partial synchronization of the mutual delay-coupled Boolean networks. The upper bound of synchronization time is obtained. Finally, an example is provided to illustrate the efficiency of the theoretical analysis.