New global stability conditions for a class of difference equations |
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Authors: | Yoshiaki Muroya Emiko Ishiwata Nicola Guglielmi |
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Affiliation: | (1) Department of Mathematics, Waseda University, Tokyo 169-8555, Japan;(2) Department of Mathematical Information Science, Tokyo University of Science, Tokyo 162-8601, Japan;(3) Dipartimento di Matematica Pura ed Applicata, Università de L’Aquila, 67100 L’Aquila, Italy |
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Abstract: | In this paper we consider some classes of difference equations, including the well-known Clark model, and study the stability of their solutions. In order to do that we introduce a property, namely semicontractivity, and study relations between ‘semi-contractive’ functions and sufficient conditions for the solution of the difference equation to be globally asymptotically stable. Moreover, we establish new sufficient conditions for the solution to be globally asymptotically stable, and we improve the ‘3/2 criteria’ type stability conditions. |
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Keywords: | Clark model global asymptotic stability semi-contractive function nonlinear difference equation |
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