Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit cycles by perturbing quadratic isochronous centers inside
  piecewise smooth polynomial differential systems   In the present paper, we study the number of zeros of the first order
Melnikov function for piecewise smooth polynomial differential system, to
estimate the number of limit cycles bifurcated from the period annulus of
quadratic isochronous centers, when they are perturbed inside the class of all
piecewise smooth polynomial differential systems of degree $n$ with the
straight line of discontinuity $x=0$. An explicit and fairly accurate upper
bound for the number of zeros of the first order Melnikov functions with
respect to quadratic isochronous centers $S_1, S_2$ and $S_3$ is provided. For
quadratic isochronous center $S_4$, we give a rough estimate for the number of
zeros of the first order Melnikov function due to its complexity. Furthermore,
we improve the upper bound associated with $S_4$, from $14n+11$ in \cite{LLLZ},
$12n-1$ in \cite{SZ} to $[(5n-5)/2]$, when it is perturbed inside all smooth
polynomial differential systems of degree $n$. Besides, some evidence on the
equivalence of the first order Melnikov function and the first order Averaged
function for piecewise smooth polynomial differential systems is found.

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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con