Title of article
On completeness of quadratic systems Original Research Article
Author/Authors
Harry Gingold، نويسنده , , Daniel Solomon، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2011
Pages
7
From page
4234
To page
4240
Abstract
A dynamical system is called complete if every solution of it exists for all t∈Rt∈R. Let KK be the dimension of the vector space of quadratic systems. The set of complete quadratic systems is shown to contain a vector subspace of dimension 2K/32K/3. We provide two proofs, one by the Gronwall lemma and the second by compactification that is capable of showing incompleteness as well. Characterization of a vector subspace of complete quadratic systems is provided. The celebrated Lorenz system for all real ranges of its parameters is shown to belong to this subspace. We also provide a sufficient condition for a system to be incomplete
Keywords
invariant set , Quadratic systems , Polynomial systems , Lorenz system , Autonomous differential equations , Asymptotic behavior , Compactification , Completeness of dynamical system
Journal title
Nonlinear Analysis Theory, Methods & Applications
Serial Year
2011
Journal title
Nonlinear Analysis Theory, Methods & Applications
Record number
863222
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