1,720,983 research outputs found
Ring wave solutions of a n+1-dimensional Sine-Gordon model
No full textThe dynamical properties of the ring wave solutions of the model psi(tt)-del(n)(2) psi+sin psi + epsilon sin (psi/2) + alpha psi(t)= 0 (0 less than or equal to epsilon much less than 1,0 less than or equal to alpha much less than 1) are studied analytically and numerically for spatial dimension (n = 2,3). The model is obtained as a continuum approximation of a multidimensional Frenkel-Kontorowa lattice. We will show that in the case epsilon>0, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of epsilon. It will be shown numerically that the dissipative perturbation alpha psi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur, (C) 1997 American Institute of Physics
Gap junctions promote synchronous activities in a network of inhibitory interneurons.
No full textBy using a single compartment biophysical model of a fast spiking interneuron the synchronization properties of a pair of cells, coupled by electrical and inhibitory synapses, are investigated. The inhibitory and excitatory synaptic couplings are modeled in order to reproduce the experimental time course of the corresponding currents. It is shown that increasing the conductance value of the electrical synapses enhances the synchronization between the spike trains of the two cells. Moreover, increasing either the decay time constant of the inhibitory current or the firing frequency of the cells favours the emergence of synchronous discharges
,Study of a C-integrable partial differential equation in Space-Time Chaos, characterization control and synchronization
No full textExistence of anticorrelations for local field potentials recorded from mice reared in standard condition and environmental enrichment
No full textIn the present paper, we analyze local field potentials (LFPs) recorded from the secondary motor cortex (M2) and primary visual cortex (V1) of freely moving mice reared in environmental enrichment (EE) and standard condition (SC). We focus on the scaling properties of the signals by using an integrated approach combining three different techniques: the Higuchi method, detrended fluctuation analysis, and power spectrum. Each technique provides direct or indirect estimations of the Hurst exponent H and this prevents spurious identification of scaling properties in time-series analysis. It is well known that the power spectrum of an LFP signal scales as 1/f(β) with β>0. Our results indicate the existence of a particular power spectrum scaling law 1/f(β) with β<0 for low frequencies (f<4 Hz) for both SC and EE rearing conditions. This type of scaling behavior is associated to the presence of anticorrelation in the corresponding LFP signals. Moreover, since EE is an experimental protocol based on the enhancement of sensorimotor stimulation, we study the possible effects of EE on the scaling properties of secondary motor cortex (M2) and primary visual cortex (V1). Notably, the difference between Hurst's exponents in EE and SC for individual cortical regions (M2) and (V1) is not statistically significant. On the other hand, using the detrended cross-correlation coefficient, we find that EE significantly reduces the functional coupling between secondary motor cortex (M2) and visual cortex (V1)
Dynamical properties of a kink of the Sine-Gordon equation trapped in a potential well
No full textThe dynamical properties of a kink of the Sine-Gordon equation trapped in a potential well and interacting with a periodic spatial inhomogeneity are investigated. It is shown that the description of the kink motion obtained by the adiabatic approximation breaks down. This fact is explained in term of changes in the kink form due to the presence of such perturbations. We will show that in the presence of spatial periodic inhomogeneity there are parameter ranges where complex behaviour of the kink dynamics is observed. Moreover, when the spatial periodic perturbation is switched off for each kink initial velocity the radiation emission corresponding to well defined wave number is inhibited
Dynamical properties of LFPs from mice with unilateral injection of TeNT
No full textLocal field potential (LFP) recordings were performed from the visual cortex (V1) of a focal epilepsy mouse model. Epilepsy was induced by a unilateral injection of the synaptic blocker tetanus neurotoxin (TeNT). LFP signals were simultaneously recorded from V1 of both hemispheres of each animal under acute and chronic conditions (i.e. during and after the period of TeNT action). All data were analysed by using nonlinear time series methods. Suitable values of the lag time and embedding dimension for phase space reconstruction were estimated by employing well-known methods. The results showed that lag times are sensitive to the presence of TeNT. Interestingly, TeNT promoted an increase in the level of linear and nonlinear correlation of LFP signals. The values of the embedding dimension failed to show any dependence on the presence of the neurotoxin. However, a local nonlinear prediction method showed that the presence of TeNT increases the predictability, quantified by the normalized prediction error, of the neural recordings. From a neurophysiological point of view, the above results suggest that TeNT injected in one hemisphere strongly impacts the local electrical activity of the neural populations in the opposite hemisphere. We hypothesize that this could arise from a qualitative and quantitative alteration of the transmission properties of the callosal fibers. (C) 2017 Elsevier B.V. All rights reserved
Phase-locking patterns in a resonate and fire neural model with periodic drive
No full textIn this paper we studied a resonate and fire relaxation oscillator subject to time dependent modulation to investigate phase-locking phenomena occurring in neurophysiological systems. The neural model (denoted LFHN) was obtained by linearization of the FitzHugh-Nagumo neural model near an hyperbolic fixed point and then by introducing an integrate-and-fire mechanism for spike generation. By employing specific tools to study circle maps, we showed that this system exhibits several phase-locking patterns in the presence of periodic perturbations. Moreover, both the amplitude and frequency of the modulation strongly impact its phase-locking properties. In addition, general conditions for the generation of firing activity were also obtained. In addition, it was shown that for moderate noise levels the phase-locking patterns of the LFHN persist. Moreover, in the presence of noise, the rotation number changes smoothly as the stimulation current increases. Then, the statistical properties of the firing map were investigated too. Lastly, the results obtained with the forced LFHN suggest that such neural model could be used to fit specific experimental data on the firing times of neurons
Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice
No full textEpilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (40 ms). Onthe other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here
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