Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volterra-series approach to stochastic nonlinear dynamics: linear
  response of the Van der Pol oscillator driven by white noise   The Van der Pol equation is a paradigmatic model of relaxation oscillations.
This remarkable nonlinear phenomenon of self-sustained oscillatory motion
underlies important rhythmic processes in nature and electrical engineering.
Relaxation oscillations in a real system are usually coupled to environmental
noise, which further enriches their dynamics, but makes theoretical analysis of
such systems and determination of the equation's parameter values a difficult
task. In a companion paper we have proposed an analytic approach to a similar
problem for another classical nonlinear model, the bistable Duffing oscillator.
Here we extend our techniques to the case of the Van der Pol equation driven by
white noise. We analyze the statistics of solutions and propose a method to
estimate parameter values from the oscillator's time series. We use
experimental data of active oscillations in a biological system to demonstrate
how our method applies to real observations and how it can be generalized for
more complex models.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg