Two types of stability conditions for linear delay difference equations | Zendy

Jan Čermák | Zendy; Jiří Jánský | Zendy; Petr Tomášek | Zendy

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Two types of stability conditions for linear delay difference equations

Author(s) -

Jan Čermák,

Jiří Jánský,

Petr Tomášek

Publication year - 2014

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm141009016c

Subject(s) - mathematics , stability (learning theory) , discretization , differential equation , characteristic equation , delay differential equation , mathematical analysis , exponential stability , type (biology) , nonlinear system , ecology , physics , quantum mechanics , machine learning , computer science , biology

The paper discusses asymptotic stability conditions for a four-parameter linear difference equation appearing in the process of discretization of a delay differential equation. We present two types of conditions, which are necessary and sufficient for asymptotic stability of the studied equation. A relationship between both the types of conditions is established and some of their consequences are discussed.

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