Related papers: On the noise modelling in a nerve fiber
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modeling approaches for the description of anomalous diffusion in biological systems, such as the very…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal…
In complex networked systems theory, an important question is how to evaluate the system robustness to external perturbations. With this task in mind, I investigate the propagation of noise in multi-layer networked systems. I find that, for…
We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing {\it finite} $N$ neurons. Calculations using the Fokker-Planck…
We study stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we…
We study and analyze the fundamental aspects of noise propagation in recurrent as well as deep, multi-layer networks. The main focus of our study are neural networks in analogue hardware, yet the methodology provides insight for networks in…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
We analyze the effects of noise on the traveling wave dynamics in neural fields. The noise influences the dynamics on two scales: first, it causes fluctuations in the wave profile, and second, it causes a random shift in the phase of the…
We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{\alpha\beta}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de…
We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…
Neural Network Potentials (NNPs) have emerged as a powerful tool for modelling atomic interactions with high accuracy and computational efficiency. Recently, denoising diffusion models have shown promise in NNPs by training networks to…
We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with…
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability…
We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the…
Neurons in the central nervous system are affected by complex and noisy signals due to fluctuations in their cellular environment and in the inputs they receive from many other cells 1,2. Such noise usually increases the probability that a…
Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
The aim of this paper is to provide a mathematical model for spatial distribution of membrane electrical potential changes by fluorescence diffuse optical tomography. We derive the resolving power of the imaging method in the presence of…