Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bursting oscillations induced by small noise   We consider a model of a square-wave bursting neuron residing in the regime
of tonic spiking. Upon introduction of small stochastic forcing, the model
generates irregular bursting. The statistical properties of the emergent
bursting patterns are studied in the present work. In particular, we identify
two principal statistical regimes associated with the noise-induced bursting.
In the first case, (type I) bursting oscillations are created mainly due to the
fluctuations in the fast subsystem. In the alternative scenario, type II
bursting, the random perturbations in the slow dynamics play a dominant role.
We propose two classes of randomly perturbed slow-fast systems that realize
type I and type II scenarios. For these models, we derive the Poincare maps.
The analysis of the linearized Poincare maps of the randomly perturbed systems
explains the distributions of the number of spikes within one burst and reveals
their dependence on the small and control parameters present in the models. The
mathematical analysis of the model problems is complemented by the numerical
experiments with a generic Hodgkin-Huxley type model of a bursting neuron.

22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol