Effects of noise in excitable systems

By Benjamin Lindner, Jordi García-Ojalvo, A. Neiman, Lutz Schimansky-Geier. 2004

1,413 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/50ba8b0c45dc5510fa7eac64ca35bacb936cd3c0

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In Cognitive Neuroscience

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics (2011, background): “Consider the following stochastic van der Pol equation (see also [58]): dxτ = 1 ǫ (”
Balanced Networks of Spiking Neurons with Spatially Dependent Recurrent Connections (2013, background): “The study of spatiotemporal dynamics and variability in complex systems is at the interface of the physical, chemical, biological, and social sciences [1,2].”
Spatiotemporal order out of noise (2007, background): “Lindner et al., 2004", and noise-induced transport !”
Strong and moderate nonlinear El Niño regimes (2016, background): “From a broader dynamical system perspective, the existence of a threshold above which enhanced positive feedbacks can lead to a strong EN suggests that the ENSO system possesses stochastic excitable dynamics (Lindner et al. 2003), where excitable refers to the enhanced responsiveness above a thresho”
Noise-Induced Phenomena in the Environmental Sciences (2011, background): “In all these fields the concept of stochastic resonance has opened new avenues for the interpretation and the control of the relevant dynamics (Lindner et al., 2004).”
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties (2006, background): “The phenomena of stochastic resonance was demonstrated in neural systems by using external noise applied to cray-ﬁsh mechanoreceptor cells (Douglas et al. 1993), and this sparked its discovery and examination in numerous other neural systems (Lindner et al. 2004).”
Excitability in ramped systems: the compost-bomb instability (2011, background): “Other possibilities include stochastic fluctuations in the system variable(s) (Lindner et al. 2004).”
Dynamical principles in neuroscience (2006, background): “There are several possible functions for noise Lindner et al., 2004 , even seen as high-dimensional essentially unpredictable chaotic motion, in neural network studies.”
Relativistic Brownian Motion (2008, background): “ing the limit t→ ∞. These asymptotic solutions are usually also time periodic and can exhibit phase shifts. They may give rise to a number of interesting phenomena such as, e.g., stochastic resonance [431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441]. From the purely mathematical perspective, S”