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Erschienen in:
Stable Bifurcations in Multi-species Semelparous Population Models Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

On the Exponential Stability of Two-Dimensional Nonautonomous Difference Systems Which Have a Weighted Homogeneity of the Solution

verfasst von : Masakazu Onitsuka

Erschienen in: Advances in Difference Equations and Discrete Dynamical Systems

Verlag: Springer Singapore

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Abstract

The present paper is considered a two-dimensional difference system:
$$\begin{aligned} \varDelta x(n) = a(n)x(n)+b(n)\phi _{p^*\!}(y(n)), \quad \varDelta y(n) = c(n)\phi _p(x(n))+d(n)y(n), \end{aligned}$$
where all coefficients are real-valued sequences; p and \(p^*\) are positive numbers satisfying \(1/p + 1/p^* = 1\); and \(\phi _p(x) = |x|^{p-2}x\) for \(x \ne 0\), and \(\phi _p(0) = 0\). The aim of this paper is to clarify that uniform asymptotic stability and exponential stability are equivalent for the above system. To illustrate the obtained results, an example is given. In addition, a figure of a solution orbit which is drawn by a computer is also attached for a deeper understanding.

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Vorheriges Kapitel On the Structure of Polyhedral Positive Invariant Sets with Respect to Delay Difference Equations
Nächstes Kapitel A Corollary of a Theorem on Positive Solutions of Poincaré Difference Equations
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Metadaten
Titel
On the Exponential Stability of Two-Dimensional Nonautonomous Difference Systems Which Have a Weighted Homogeneity of the Solution
verfasst von
Masakazu Onitsuka
Copyright-Jahr
2017
Verlag
Springer Singapore
Buch
Advances in Difference Equations and Discrete Dynamical Systems

Print ISBN: 978-981-10-6408-1

Electronic ISBN: 978-981-10-6409-8

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-981-10-6409-8_11