相关论文: Networks of piecewise linear neural mass models

Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

We present a formal, mathematical foundation for modeling and reasoning about the behavior of $synchronous$, $stochastic$ $Spiking$ $Neural$ $Networks$ $(SNNs)$, which have been widely used in studies of neural computation. Our approach…

We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the…

We introduce OS-net (Orbitally Stable neural NETworks), a new family of neural network architectures specifically designed for periodic dynamical data. OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and takes…

We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…

Delay-coupled systems often require low-latency decisions from sparse telemetry, where dense fixed-step neural inference is wasteful and can degrade near stability margins. We introduce Network-Optimised Spiking (NOS), a trainable two-state…

A diverse white matter network and finely tuned neuronal membrane properties allow the brain to transition seamlessly between cognitive states. However, it remains unclear how static structural connections guide the temporal progression of…

Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…

Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing…

Real neurons connect to each other non-randomly. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin-Huxley model, or the Morris-Lecar model, impacts synchronizability remains unknown. One powerful…

Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…

Examining emotion interactions as an emotion network in social media offers key insights into human psychology, yet few studies have explored how fluctuations in such emotion network evolve during crises and normal times. This study…

Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call…

It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by…

We have investigated the role that different connectivity regimes play on the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random connectivity…

We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians,…

We investigate the linear Floquet stability of two fluid layers undergoing oscillations in the direction parallel to the flexible wall that separates them. This canonical configuration is inspired by the cerebrospinal fluid flow in the…