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Hodgkin-Huxley equations as a monumental breakthrough in biological and physiological theory of the 20th century had been distilled into many simplified models to study, typically FitzHugh-Nagumo equations and Hindmarsh-Rose equations, but…
Demystifying effective connectivity among neuronal populations has become the trend to understand the brain mechanisms of Parkinson's disease, schizophrenia, mild traumatic brain injury, and many other unlisted neurological diseases.…
Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory has been developed mostly for smooth dynamical systems and…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics…
Depression is a very common but serious mood disorder.In this paper, We built a generative detection network(GDN) in accordance with three physiological laws. Our aim is that we expect the neural network to learn the relevant brain activity…
Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many…
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…
Small continuous sensory and mechanical perturbations have often been used to identify properties of the closed-loop neural control of posture and other systems that are approximately linear time invariant. Here we extend this approach to…
We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…
The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is…
Driver drowsiness electroencephalography (EEG) signal monitoring can timely alert drivers of their drowsiness status, thereby reducing the probability of traffic accidents. Graph convolutional networks (GCNs) have shown significant…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
Overparameterized neural networks often contain many removable neurons, yet what makes a neuron redundant remains poorly understood. Existing pruning criteria commonly rely on local quantities such as weight magnitude, activation strength,…
Despite recent advances in brain research, understanding the various signals for pain and pain intensities in the brain cortex is still a complex task due to temporal and spatial variations of brain hemodynamics. In this paper we have…
We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a…
The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according…
Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural…
Neurostimulation technologies have seen a recent surge in interest from the neuroscience and controls communities alike due to their proven potential to treat conditions such as Parkinson's Disease, and depression. The provided stimulation…
Spiking Neural Networks (SNNs) currently face a critical bottleneck: while individual neurons exhibit dynamic biological properties, their macro-scopic architectures remain confined within conventional connectivity patterns that are static…