Stability and periodic investigations of linear planar difference systems

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• 作者：Jan Čerm&aacute ; k and Jiří ; J&aacute ; nský
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：39
• 期：18
• 页码：5343-5354
• 全文大小：624K
• ISSN：1099-1476

文摘

This paper discusses the problem of stability and periodic behaviour of linear planar difference systems appearing in modelling of discrete problems of population biology and Hopfield neural networks. We concentrate especially on procedures, which enable to formulate optimal (i.e. necessary and sufficient) conditions guaranteing such a behaviour. As a main tool, we analyse in detail location of zeros of characteristic polynomials with respect to the unit circle. From this viewpoint, derived results contribute also to the polynomial theory. Copyright