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PACS. 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 82.20.Mj Nonequilibrium kinetics,

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 mean activity demonstrates the high efficiency of the transmission of a noise coded signal in a broad frequency band. For both kinds of signal we show that the transmission by the ensemble reveals stochastic resonance as well as a nonmonotonous dependence on the driving frequency.

Recent studies suggest that noncooperative behavior such as cannibalism may be a driving mechanism of collective motion. Motivated by these novel results we introduce a simple model of Brownian particles interacting by biologically motivated pursuit and escape interactions. We show the onset of collective motion for both interaction types and analyze their impact on the global dynamics. We demonstrate a strong dependence of experimentally accessible macroscopic observables on the relative strength of escape and pursuit and determine the scaling of the migration speed with model parameters.

We study the diffusive motion of an overdamped Brownian particle in a tilted periodic potential. Mapping the continuous dynamics onto a discrete cumulative process we find exact expressions for the diffusion coefficient and the Péclet number which characterize the transport. At a sufficiently strong but subcritical bias an optimized transport with respect to the noise strength is observed. These results are confirmed by numerical solution of the Fokker-Planck equation.

Inspired by the Turing mechanism for pattern formation, we propose a simple self-propelled particle model with short-ranged alignment and anti-alignment at larger distances. It is able to produce orientationally ordered states, periodic vortex patterns as well as meso-scale turbulence. The latter phase resembles observations in dense bacterial suspensions. The model allows a systematic derivation and analysis of a kinetic theory as well as hydrodynamic equations for density and momentum fields. A phase diagram with regions of such pattern formation as well as spatially homogeneous orientational order and disorder is obtained from a linear stability analysis of these continuum equations. Microscopic Langevin simulations of the self-propelled particle system are in agreement with these findings.The term active matter refers to non-equilibrium systems of interacting, self-propelled entities which are able to take up energy from their environment and convert it into motion [1,2]. Examples, such as cytoskeletal filaments [3], chemically driven colloids [4] or flocks of birds [5] have recently received a lot of attention in physics, chemistry and biology. They exhibit a wide range of collective phenomena which are absent in systems at thermodynamic equilibrium, for example large-scale travelling bands and polar clusters [6,7] as well as arrays of vortices [8,9]. In this context, bacteria represent important model systems, which have been used to investigate such different aspects as clustering [10] and rheological properties [11] of active matter systems.Recently, irregular vortex structures were experimentally observed in dense bacterial suspensions [11][12][13][14][15]. In addition, a phenomenological model was proposed which describes the observed behavior including the power spectrum of the bacterial dynamics [14,16]. The spectrum at large wave numbers as well as the dynamic vortex patterns in these experiments and simulations are reminiscent of a turbulent state which led the authors to denominate this new phenomenon as "meso-scale turbulence".We aim to formulate a model at the level of individual particles which is capable to produce such mesoscopic spatiotemporal patterns. Inspired by the Turing mechanism of short-range activation and long-range inhibition in reaction-diffusion systems [17,18], we propose interacting self-propelled particles with local alignment at short length scales and anti-alignment at larger distances. Such a type of interactions may be realized by a competition of local alignment and large-scale hydrodynamic back-flow effects [19,20], e. g. in suspensions of bacterial microswimmers, which leads to preferential alignment of neighboring cells and anti-alignment with more distant swimmers.Here, we abstain from considering a detailed model of individual swimmers immersed and interacting through a surrounding fluid. Our model includes effective interactions of self-propelled particles of the type first formulated by Vicsek et al. [21]. The original Vicsek model displays surprisingly complex sp...

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 deviation are investigated. The latter quantities allow a quantitative description of the phenomenon of coherence resonance, as comparisons with simulations show.