Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical Calculation of Critical Perturbation Amplitudes and Critical
  Densities by Non-Linear Stability Analysis of a Simple Traffic Flow Model   Driven many-particle systems with nonlinear interactions are known to often
display multi-stability, i.e. depending on the respective initial condition,
there may be different outcomes. Here, we study this phenomenon for traffic
models, some of which show stable and linearly unstable density regimes, but
areas of metastability in between. In these areas, perturbations larger than a
certain critical amplitude will cause a lasting breakdown of traffic, while
smaller ones will fade away. While there are common methods to study linear
instability, non-linear instability had to be studied numerically in the past.
Here, we present an analytical study for the optimal velocity model with a
stepwise specification of the optimal velocity function and a simple kind of
perturbation. Despite various approximations, the analytical results are shown
to reproduce numerical results very well.

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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat