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A new view on one problem of asymptotic behavior of solutions of delay difference equations

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  • L. Shaikhet

Abstract

One known theorem on the asymptotic behavior of solution of linear delay difference equation is considered where a stability criterion is derived via a positive root of the corresponding characteristic equation. Two new directions for further investigation are proposed. The first direction is connected with a weakening of the known stability criterion; the second one is connected with consideration of negative and complex roots of the characteristic equation. A lot of pictures with stability regions and trajectories of considered processes are presented for visual demonstration of the proposed directions.

Suggested Citation

  • L. Shaikhet, 2006. "A new view on one problem of asymptotic behavior of solutions of delay difference equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-16, June.
    • Handle: RePEc:hin:jnddns:074043
    DOI: 10.1155/DDNS/2006/74043
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