Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noise induced Hopf bifurcation   We consider effect of stochastic sources upon self-organization process being
initiated with creation of the limit cycle induced by the Hopf bifurcation.
General relations obtained are applied to the stochastic Lorenz system to show
that departure from equilibrium steady state can destroy the limit cycle in
dependence of relation between characteristic scales of temporal variation of
principle variables. Noise induced resonance related to the limit cycle is
found to appear if the fastest variations displays a principle variable, which
is coupled with two different degrees of freedom or more.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: nlin