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We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing or oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations, hence destroying the stable limit cycle. Further application of the noise may return the system to spiking activity. In a particular noise range, the transition times between the oscillating and the resting state are strongly asymmetric. We numerically investigate an approximate basin of attraction, A, of the periodic orbit and use Markov process theory to explain the firing behavior in terms of the probability of escape of trajectories from A
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal description of neu
The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects of stochastic spiking neurons such as
We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, i
Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several int