On global asymptotic stability of nonlinear higher-order difference equations (Q413720)
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scientific article; zbMATH DE number 6031324
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On global asymptotic stability of nonlinear higher-order difference equations |
scientific article; zbMATH DE number 6031324 |
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On global asymptotic stability of nonlinear higher-order difference equations (English)
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7 May 2012
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The authors generalize the main theorem of \textit{E. Liz} and \textit{J. B. Ferreiro} [Appl. Math. Lett. 15, No. 6, 655--659 (2002; Zbl 1036.39013)] and some other global stability results for nonautonomous higher-order difference equations to the case when contraction-type steps are incorporated together with the steps when the difference sequence can increase. The relation to the \(\theta \)-method for discretization of delay equations is discussed, and some sufficient stability conditions for the numerical scheme are deduced.
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nonlinear difference equations
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higher-order difference equations
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global asymptotic stability
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\(\theta \)-method
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discretizations of delay equations
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