Stochastic integrate & fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g. two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.

Integrate-and-fire (IF) neurons have found widespread applications in computational neuroscience. Particularly important are stochastic versions of these models where the driving consists of a mean input (base current µ) and a fluctuating current (white Gaussian noise of intensity D). Different IF models have been proposed, the firing statistics of which depends nontrivially on the input parameters µ and D. Comparison of these models among each other or with real neurons should be performed at parameters that yield similar basic firing statistics as, for instance, the firing rate and the coefficient of variation (CV) of the interspike interval. However, it is not clear a priori whether for a given firing rate and CV, there is only one unique choice of input parameters for the respective model. Here we review the dependence of rate and CV on input parameters for the perfect, leaky, and quadratic IF neuron models and show analytically that indeed in all three models the firing rate and the CV of the interspike interval distribution uniquely determine the input parameters. For the leaky and quadratic IF models, we use properties of the contour lines for fixed rate and CV and also give simple numerical algorithms leading from given rate and CV to the actual input parameters.

The fate of aerosols in open flows is relevant in a variety of physical contexts. Previous results are consistent with the assumption that such finite-size particles always escape in open chaotic advection. Here we show that a different behavior is possible. We analyze the dynamics of aerosols both in the absence and presence of gravitational effects, and both when the dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent trapping of aerosols much heavier than the advecting fluid is shown to occur in all these cases. This phenomenon is determined by the occurrence of multiple vortices in the flow and is predicted to happen for realistic particle-fluid density ratios.

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in raindrop statistics and in stirring tank experiments.