Integrability of the Hide-Skeldon-Acheson dynamo

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• 作者：Adam Mahdip>ap>p> ; p>p>bp>p> ; p>p>amahdi@ncsu.edu" class="auth_mailp> ; Claudia Vallsp>cp>p> ; p>p>cvalls@math.ist.utl.pt" class="auth_mailp>
• 关键词：34C05 ; 34A34
• 刊名：Bulletin des Sciences Mathematiques
• 出版年：June 2014
• 年：2014
• 卷：138
• 期：4
• 页码：470-482
• 全文大小：243 K

文摘

In this work we consider the Hide–Skeldon–Acheson dynamo model where 伪  , 尾  , 魏   and 位   are parameters. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. Provided pan id="mmlsi2" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0007449713000407&_mathId=si2.gif&_user=111111111&_pii=S0007449713000407&_rdoc=1&_issn=00074497&md5=8d8ecf97fab7e584040b302c2a9e5918" title="Click to view the MathML source">伪≠0pan>pan class="mathContainer hidden">pan class="mathCode">$伪\ne 0$pan>pan>pan> we identify the values of the parameters of this model, for which it admits a first integral. Also, as a corollary of our main results we get that for pan id="mmlsi3" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0007449713000407&_mathId=si3.gif&_user=111111111&_pii=S0007449713000407&_rdoc=1&_issn=00074497&md5=92e8f73e43c3ce1f54f3694519774f63" title="Click to view the MathML source">伪,尾,魏≠0pan>pan class="mathContainer hidden">pan class="mathCode">$伪,尾,魏\ne 0$pan>pan>pan> the dynamo model does not admit a polynomial, rational or Darboux first integral.