Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equation of the Aftershocks and its Phase Portrait   Recently, simple differential models of aftershocks have attracted increased
attention of researchers at the Institute of Physics of the Earth, Russian
Academy of Sciences for their remarkable properties. The shortened Bernoulli
equation allows us to introduce the concept of the source deactivation factor
and phenomenologically describe the nonstationarity of the geological
environment in the earthquake source, "cooling down" after the main shock. The
Verhulst logistic equation makes it possible to take into account the
transition of the aftershock flow to the background seismicity mode. The
Kolmogorov-Petrovsky-Piskunov nonlinear diffusion equation is convenient for
modeling the spatio-temporal evolution of aftershocks. This paper focuses on
the phase portrait of a dynamical system that simulates the evolution of
aftershocks. The phase portrait allows us to understand why the Omori
hyperbolic law is most clearly manifested after strong earthquakes. It is noted
that the Omori epoch, during which the deactivation coefficient is constant,
does not immediately end with a transition to the background mode. In the
experience after the end of the Omori epoch, the deactivation coefficient
changes over time in a rather complex way, and can even becomes negative. The
theory predicts that if negative values of the coefficient are held long
enough, then a geotectonic explosion occurs, vaguely resembling the main shock
of earthquake. The paper discusses possible directions for the further
development of the theory. Keywords: earthquake, aftershock, deactivation
factor, Omori epoch, logistic equation, explosive instability, Bath law.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
16
The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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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: cs
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin