相关论文: Simulating brain rhythms using an ODE with stochas…

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good…

Electrophysiological brain signals, such as electroencephalography (EEG), exhibit both periodic and aperiodic components, with the latter often modeled as 1/f noise and considered critical to cognitive and neurological processes. Although…

In sensory neurons the presence of noise can facilitate the detection of weak information-carrying signals, which are encoded and transmitted via correlated sequences of spikes. Here we investigate relative temporal order in spike sequences…

We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to…

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a…

We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…

Despite intensive research, the mechanisms underlying how neurons encode external inputs remain poorly understood. Recent work has focused on the response of a single neuron to a weak, subthreshold periodic signal. By simulating the…

This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a…

We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…

The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single…

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…

Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The…

We consider a stochastic perturbation of a FitzHugh-Nagumo system. We show that it is possible to generate oscillations for values of parameters which do not allow oscillations for the deterministic system. We also study the appearance of a…

The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…

Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statistical and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, correlation dimension…

Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally…

Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic…