Related papers: Global dynamics of neural mass models

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…

The neocortex, a complex system driving multi-region interactions, remains a core puzzle in neuroscience. Despite quantitative insights across brain scales, understanding the mechanisms underlying neural activities is challenging. Advances…

In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…

Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that…

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Whether, when, and how causal interactions between neurons can be meaningfully studied from observations of neural activity alone are vital questions in neural data analysis. Here we aim to better outline the concept of functional…

This paper proposes a class of neural ordinary differential equations parametrized by provably input-to-state stable continuous-time recurrent neural networks. The model dynamics are defined by construction to be input-to-state stable (ISS)…

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.…

We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…

Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…

In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…

Neurodegenerative diseases are characterized by the accumulation of misfolded proteins and widespread disruptions in brain function. Computational modeling has advanced our understanding of these processes, but efforts have traditionally…

We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…

Empirical estimates of the dimensionality of neural population activity are often much lower than the population size. Similar phenomena are also observed in trained and designed neural network models. These experimental and computational…

Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…

Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally. Moreover, selecting a suitable model complexity requires a…

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them.…

The traditional view of neural computation in the cerebral cortex holds that sensory neurons are specialized, i.e., selective for certain dimensions of sensory stimuli. This view was challenged by evidence of contextual interactions between…