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Wyniki wyszukiwania dla: INTEGRATE-AND-FIRE
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Integrate-and-fire models with an almost periodic input function
PublikacjaWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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On the interspike-intervals of periodically-driven integrate-and-fire models
PublikacjaWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive
PublikacjaWe study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublikacjaWe consider the Leaky Integrate-and-Fire and Perfect Integrator models of neuron’s dynamics with the input function being periodic and almost-periodic (in the sense of Stepanov). In particular we analyze properties and dynamics of the so-called firing map, which iterations give timings of consecutive spikes of a neuron. In case of a periodic input function we provide a detailed description of the sequence of interspike-intervals,...
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Firing map of an almost periodic input function
PublikacjaIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Distribution of the displacement sequence of an orientation preserving circle homeomorphism
PublikacjaIn some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...
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Adjusted SpikeProp algorithm for recurrent spiking neural networks with LIF neurons
PublikacjaA problem related to the development of a supervised learning method for recurrent spiking neural networks is addressed in the paper. The widely used Leaky-Integrate-and-Fire model has been adopted as a spike neuron model. The proposed method is based on a known SpikeProp algorithm. In detail, the developed method enables gradient descent learning of recurrent or multi-layer feedforward spiking neural networks. The research included...