Synaptic dependence of dynamic regimes when coupling neural populations.

In this article we focus on the study of the collective dynamics of neural networks. The analysis of two recent models of coupled "next-generation" neural mass models allows us to observe different global mean dynamics of large neural populations. These models describe the mean dynamics of all-to-all coupled networks of quadratic integrate-and-fire spiking neurons. In addition, one of these models considers the influence of the synaptic adaptation mechanism on the macroscopic dynamics. We show how both models are related through a parameter and we study the evolution of the dynamics when switching from one model to the other by varying that parameter. Interestingly, we have detected three main dynamical regimes in the coupled models: Rössler-type (funnel type), bursting-type, and spiking-like (oscillator-type) dynamics. This result opens the question of which regime is the most suitable for realistic simulations of large neural networks and shows the possibility of the emergence of chaotic collective dynamics when synaptic adaptation is very weak.

Deep Learning for chaos detection.

In this article, we study how a chaos detection problem can be solved using Deep Learning techniques. We consider two classical test examples: the Logistic map as a discrete dynamical system and the Lorenz system as a continuous dynamical system. We train three types of artificial neural networks (multi-layer perceptron, convolutional neural network, and long short-term memory cell) to classify time series from the mentioned systems into regular or chaotic. This approach allows us to study biparametric and triparametric regions in the Lorenz system due to their low computational cost compared to traditional techniques.