The Study of Generalized Synchronization between Two Identical Neurons Based on the Laplace Transform Method

In this paper, a new method is proposed based on the auxiliary system approach to investigate generalized synchronization between two identical neurons with unidirectional coupling. Different from other studies, the synchronization error system between the response and auxiliary systems is converted into a set of Volterra integral equations according to the Laplace transform method and convolution theorem. By using the successive approximation method in the theory of integral equations, an analytical criterion for the detection of generalized synchronization between two identical neurons is obtained. It is found that there is a time difference between two signals of neurons when the generalized synchronization between them is achieved. Furthermore, the value of the time difference has no relation to the generalized synchronization condition but depends on the coupling function between two neurons. The study in this paper shows that one can construct a coupling function between two identical neurons using the current signal of the drive system to predict its future signal or make its past signal reappear.

The interaction between neural populations: Additive versus diffusive coupling

Models of networks of populations of neurons commonly assume that the interactions between neural populations are via additive or diffusive coupling. When using the additive coupling, a population's activity is affected by the sum of the activities of neighbouring populations. In contrast, when using the diffusive coupling a neural population is affected by the sum of the differences between its activity and the activity of its neighbours. These two coupling functions have been used interchangeably for similar applications. Here, we show that the choice of coupling can lead to strikingly different brain network dynamics. We focus on a model of seizure transitions that has been used both with additive and diffusive coupling in the literature. We consider networks with two and three nodes, and large random and scale-free networks with 64 nodes. We further assess functional networks inferred from magnetoencephalography (MEG) from people with epilepsy and healthy controls. To characterize the seizure dynamics on these networks, we use the escape time, the brain network ictogenicity (BNI) and the node ictogenicity (NI), which are measures of the network's global and local ability to generate seizures. Our main result is that the level of ictogenicity of a network is strongly dependent on the coupling function. We find that people with epilepsy have higher additive BNI than controls, as hypothesized, while the diffusive BNI provides the opposite result. Moreover, individual nodes that are more likely to drive seizures with one type of coupling are more likely to prevent seizures with the other coupling function. Our results on the MEG networks and evidence from the literature suggest that the additive coupling may be a better modelling choice than the diffusive coupling, at least for BNI and NI studies. Thus, we highlight the need to motivate and validate the choice of coupling in future studies.

Synchronisation Conditions for a Class of Non-linearly Coupled Networks using Contraction Based Strategy

This paper describes a simple and general framework for synchronisation of non-linearly coupled dynamical systems interconnected to constitute a com- plex network. The proposed methodology of attaining synchronisation of networks is based on contraction strat- egy. The paper introduces a systematic control proce- dure to achieve synchronisation of a coupled dynamical network of proposed strict-feedback like class of nonlin- ear systems. The non-linear coupling function between different systems of the network is assumed to be in the form of bidirectional links. The proposed method- ology can be applicable to any arbitrarily structure of linear/non-linear, bidirectional or unidirectional N- coupled systems in a network. The general results have been derived for coupled systems interacting through nonlinear coupling function which are interconnected in different networked topologies including Ring, Global, Star, Arbitrary etc. The analytical conditions for syn- chronisation are expressed in terms of bounds on cou- pling strength which are derived using partial contrac- tion concepts blended with graph theory results. The proposed approach is straightforwardly applied to high dimensional non-linearly coupled chaotic systems which are common in many applications. A set of representa- tive examples of coupled chaotic systems based network are simulated to verify the theoretical results.

Explicit IMF By-dependence in geomagnetic activity

<p>The interaction of the solar wind with the Earth’s magnetic field produces geomagnetic activity, which is critically dependent on the orientation of the interplanetary magnetic field (IMF). Most solar wind coupling functions quantify this dependence on the IMF orientation with the so-called IMF clock angle in a way, which is symmetric with respect to the sign of the B<sub>y</sub> component. However, recent studies have shown that IMF B<sub>y</sub> is an additional, independent driver of high-latitude geomagnetic activity, leading to higher (weaker) geomagnetic activity in Northern Hemisphere (NH) winter for B<sub>y</sub> > 0 (B<sub>y</sub> < 0). For NH summer the dependence on the B<sub>y</sub> sign is reversed. We quantify the size of this explicit B<sub>y</sub>-effect with respect to the solar wind coupling function, both for northern and southern high-latitude geomagnetic activity. We show that for a given value of solar wind coupling function, geomagnetic activity is about 40% stronger for B<sub>y</sub> > 0 than for B<sub>y</sub> < 0 in NH winter. We also discuss recent advances in the physical understanding of the B<sub>y</sub>-effect. Our results highlight the importance of the IMF B<sub>y</sub>-component for space weather and must be taken into account in future space weather modeling.</p>

Quasinormal modes of hot, cold and bald Einstein–Maxwell-scalar black holes

Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function $$f(\phi )$$ f ( ϕ ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, $$f(\phi )=1+\alpha \phi ^4$$ f ( ϕ ) = 1 + α ϕ 4 (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

On the Need to Reparametrize the OVATION Prime (2010) Auroral Precipitation Model

The need to reparametrize the OVATION Prime (2010) empirical auroral precipitation model using the Russian polar cap index (PC index) is considered. For this purpose, the integrated auroral power of particle precipitation obtained from the Polar satellite data for the period from December 1996 to June 1998 is compared with the PC index and the Newell’s coupling function. The analysis revealed that the PC index at the time delays up to 5–20 minutes correlates with the magnitude of auroral power much better (the correlation coefficient R ~ 0.76–0.87) than the Newell’s coupling function (R ~ 0.46–0.82). Thus, for the purpose of nowcasting the zone of active particle precipitation, the PC index showed much higher scores, although the predicting abilities of the Newell’s coupling function for the time delays of more than 20 minutes remain the best.