Bifurcation analysis of two coupled Jansen-Rit neural mass models

We investigate how changes in network structure can lead to pathological oscillations similar to those observed in epileptic brain. Specifically, we conduct a bifurcation analysis of a network of two Jansen-Rit neural mass models, representing two cortical regions, to investigate different aspects of its behavior with respect to changes in the input and interconnection gains. The bifurcation diagrams, along with simulated EEG time series, exhibit diverse behaviors when varying the input, coupling strength, and network structure. We show that this simple network of neural mass models can generate various oscillatory activities, including delta wave activity, which has not been previously reported through analysis of a single Jansen-Rit neural mass model. Our analysis shows that spike-wave discharges can occur in a cortical region as a result of input changes in the other region, which may have important implications for epilepsy treatment. The bifurcation analysis is related to clinical data in two case studies

Bifurcation properties of the average activity of interconnected neural populations

Abstract.: The relevant scale for the study of the electrical activity of neural networks is a problem of mathematical and biological interest. From a continuous model of the cortex activity we derive a simple model of an interconnected pair of excitatory and inhibitory neural populations that describes the activity of a homogeneous network. Our model depends on three parameters that stand for the scale variability of the network. A bifurcation analysis reveals a great variety of patterns that arise from the interplay of excitatory and inhibitory populations provided by synaptic interactions. We emphasize the differences between the dynamical regimes when considering a moderate and a high inhibitory scale. We discuss the consequences on a propagating activit

Understanding the impact of recurrent interactions on population tuning: Application to MT cells characterization

International audienceA ring network model under neural fields formalism with a structured input is studied. Bifurcation analysis is applied to understand the behaviour of the network model under different connectivity regimes and input conditions. The parameter regimes over which the localised input bumps could be preserved, combined or selected are used to identify the potential network regimes under which direction selective cells in MT area exhibiting analogous behaviour could be operating. The parameter regimes are further explored to identify possible transitions in the tuning behaviour with respect to change of driving stimuli as observed in experimental recordings

The complexity of dynamics in small neural circuits

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of figures 8 and 9 fixed, results unchange

A new method of vascular point detection using artificial neural network

Vascular intersection is an important feature in retina fundus image (RFI). It can be used to monitor the progress of diabetes hence accurately determining vascular point is of utmost important. In this work a new method of vascular point detection using artificial neural network model has been proposed. The method uses a 5×5 window in order to detect the combination of bifurcation and crossover points in a retina fundus image. Simulated images have been used to train the artificial neural network and on convergence the network is used to test (RFI) from DRIVE database. Performance analysis of the system shows that ANN based technique achieves 100% accuracy on simulated images and minimum of 92% accuracy on RFI obtained from DRIVE database

Hopf Bifurcation and Chaos in Tabu Learning Neuron Models

In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. We give a numerical example to verify the theoretical analysis. Then, we demonstrate the chaotic behavior in such a neuron with sinusoidal external input, via computer simulations. Finally, we study the chaotic behaviors in tabu learning two-neuron models, with linear and quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of Bifurcation and Chao