Related papers: On the noise modelling in a nerve fiber

The dynamics of soliton molecules in ultrafast fiber ring laser cavity is strongly influenced by noise. We show how a parsimonious Langevin model can be constructed from experimental data, resulting in a mathematical description that…

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh-Nagumo system, describing the nerve impulse propagation in…

The ability to quantify stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally…

We discuss two aspects, the in vivo and in vitro difference and the modeling of noise, of integrative modeling of network dynamics in biology, using phage lambda as an example. We believe those two aspects have not been seriously…

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…

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…

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree…

Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major…

Noise is one of the primary sources of interference in seismic exploration. Many authors have proposed various methods to remove noise from seismic data; however, in the face of strong noise conditions, satisfactory results are often not…

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…

In this paper, we propose a shot noise-based leaky integrated and firing neuron model and provide a detailed analysis of the performance of this model compared to the traditional diffusion approximated model. In theoretical neuroscience,…

Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that…

A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…

We use a model based on the fractional Langevin equation with external noise to describe the anomalous dynamics observed in microrheology experiments in living cells. This model reproduces both the subdiffusive short-time and the…

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…

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and close states of ion channels. Although it has previously been shown that channel noise can nontrivially…

The dynamics of an initial wave packed affected by random noise is considered in the framework of a comb model. The model is relevant to a diffusion problem in neurons where the transport of ions can be accelerated by an external random…

In this study we give a geometrical model which employs the smoothness of nerve fibers as differentiable curves. We show that a nerve fiber may encounter large curvature due to the possible helicial bending and hence it could cause the…

The transport of molecules through biological and synthetic nanopores is governed by multiple stochastic processes that lead to noisy, fluctuating currents. Disentangling the characteristics of different noise-generating mechanisms is…