相关论文: Global-in-time classical solutions and qualitative…

The combination of new recording techniques in neuroscience and powerful inference methods recently held the promise to recover useful effective models, at the single neuron or network level, directly from observed data. The value of a…

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this…

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…

We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of…

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…

The brain-inspired Spiking Neural Networks (SNNs) have garnered considerable research interest due to their superior performance and energy efficiency in processing temporal signals. Recently, a novel multi-compartment spiking neuron model,…

Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…

We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of…

We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…

This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…

We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…

We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the…

A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…

Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to…

In this paper, a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity under initial-boundary condition is investigated. Based on potential well method and Hardy-Sobolev inequality, the global…

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function,…

We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…

In the rapidly advancing field of neuromorphic computing, integrating biologically-inspired models like the Leaky Integrate-and-Fire Astrocyte (LIFA) into spiking neural networks (SNNs) enhances system robustness and performance. This paper…

In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…