Stability chart for the delayed Mathieu equation

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Insperger T. and Stépán G. 2002Stability chart for the delayed Mathieu equationProc. R. Soc. Lond. A.4581989–1998http://doi.org/10.1098/rspa.2001.0941SectionRestricted accessStability chart for the delayed Mathieu equation T. Insperger T. Insperger Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1521, Hungary (; ) Google Scholar Find this author on PubMed Search for more papers by this author and G. Stépán G. Stépán Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1521, Hungary (; ) Google Scholar Find this author on PubMed Search for more papers by this author T. Insperger T. Insperger Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1521, Hungary (; ) Google Scholar Find this author on PubMed Search for more papers by this author and G. Stépán G. Stépán Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1521, Hungary (; ) Google Scholar Find this author on PubMed Search for more papers by this author Published:08 August 2002https://doi.org/10.1098/rspa.2001.0941AbstractIn the space of system parameters, the closed–form stability chart is determined for the delayed Mathieu equation defined as ä(t)+(δ+εcost)x(t) = bx(t−2π). This stability chart makes the connection between the Strutt–Ince chart of the Mathieu equation and the Hsu–Bhatt–Vyshnegradskii chart of the second–order delay–differential equation. The combined chart describes the intriguing stability properties of a class of delayed oscillatory systems subjected to parametric excitation. 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