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- B Lindner, L Schimansky-Geier
- Physical review letters
- 2001

Neuronal populations receive signals through temporally inhomogeneous spike trains which can be approximated by an input consisting of a time dependent mean value (additive signal) and noise with a time dependent intensity (noise coded signal). We compare the linear response of an ensemble of model neurons to these signals. Our analytical solution for the… (More)

- Benjamin Lindner, Lutz Schimansky-Geier, André Longtin
- Physical review. E, Statistical, nonlinear, and…
- 2002

We study noise-induced resonance effects in the leaky integrate-and-fire neuron model with absolute refractory period, driven by a Gaussian white noise. It is demonstrated that a finite noise level may either maximize or minimize the regularity of the spike train. We also partition the parameter space into regimes where either or both of these effects… (More)

- A Neiman, L Schimansky-Geier, F Moss, B Shulgin, J J Collins
- Physical review. E, Statistical physics, plasmas…
- 1999

We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching… (More)

- Sepideh Bazazi, Pawel Romanczuk, +6 authors Iain D Couzin
- Proceedings. Biological sciences
- 2011

In order to move effectively in unpredictable or heterogeneous environments animals must make appropriate decisions in response to internal and external cues. Identifying the link between these components remains a challenge for movement ecology and is important in understanding the mechanisms driving both individual and collective motion. One accessible… (More)

- T A Engel, L Schimansky-Geier, A V M Herz, S Schreiber, I Erchova
- Journal of neurophysiology
- 2008

Many neurons exhibit subthreshold membrane-potential resonances, such that the largest voltage responses occur at preferred stimulation frequencies. Because subthreshold resonances are known to influence the rhythmic activity at the network level, it is vital to understand how they affect spike generation on the single-cell level. We therefore investigated… (More)

- T Verechtchaguina, I M Sokolov, L Schimansky-Geier
- Physical review. E, Statistical, nonlinear, and…
- 2006

Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for non-Markovian differentiable random processes. We start from an exact expression for the FPT density in terms of an infinite series of integrals over joint densities of level crossings, and consider different approximations based on… (More)

- Tilo Schwalger, Lutz Schimansky-Geier
- Physical review. E, Statistical, nonlinear, and…
- 2008

We analytically investigate the interspike interval (ISI) density, the Fano factor, and the coefficient of variation of a leaky integrate-and-fire neuron model driven by exponentially correlated Gaussian noise with a large correlation time tau . We find a burstinglike behavior of the spike train, which is revealed by a dominant peak of the ISI density at… (More)

- Tatiana A Engel, Brian Helbig, David F Russell, Lutz Schimansky-Geier, Alexander B Neiman
- Physical review. E, Statistical, nonlinear, and…
- 2009

We study the effect of noisy oscillatory input on the signal discrimination by spontaneously firing neurons. Using analytically tractable model, we contrast signal detection in two situations: (i) when the neuron is driven by coherent oscillations and (ii) when the coherence of oscillations is destroyed. Analytical calculations revealed a region in the… (More)

- B Lindner, L Schimansky-Geier
- Physical review. E, Statistical physics, plasmas…
- 1999

We consider the FitzHugh-Nagumo system under the influence of white Gaussian noise in the excitable regime. We present an analytical approximation in the limit of fast activator time scale. Marginal probability densities of a reduced system and dynamical quantities such as the pulse rate are found and the mean interspike interval and its relative standard… (More)

- M A Zaks, A B Neiman, S Feistel, L Schimansky-Geier
- Physical review. E, Statistical, nonlinear, and…
- 2003

We derive in Gaussian approximation dynamical equations for the first two cumulants of the mean field fluctuations in a system of globally coupled stochastic phase oscillators. In these equations the intensity of noise serves as an explicit control parameter. Its variation generates transitions between three dynamical regimes: (i) stationary, (ii) rotatory… (More)