Related papers: Bursting oscillations induced by small noise
A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that takes short-term synaptic plasticity into account. The one being used here is particularly important, as it represents an exact…
The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is…
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials, in parameter regimes characterised by mixed-mode oscillations. The interspike time interval is related to the random number of…
Cultures of neurons grown on multi-electrode arrays have become a common experimental preparation for investigating developing neural networks. Experiment and simulation have shown that these developing networks eventually exhibit bursting…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue-like wave dynamics in a reaction-diffusion system…
Recently created diffusive memristors have garnered significant research interest owing to their distinctive capability to generate a diverse array of spike dynamics which are similar in nature to those found in biological cells. This gives…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
The simple system composed of three neural-like noisy elements is considered. Two of them (sensory neurons or sensors) are stimulated by noise and periodic signals with different ratio of frequencies, and the third one (interneuron)…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Young pulsars deviate from a perfectly regular spin-down by two non-deterministic phenomena: impulsive glitches and timing noise. Both phenomena are interesting per se, and may provide insights into the superfluid properties of neutron…
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity…
We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified…