The system stability of dynamic processes
type: Item
instance of: scholarly article
title: The system stability of dynamic processes
zbMATH Open document ID: 0943.91047
DOI: 10.1016/S0304-4068(97)00008-6
author: Akitaka Dohtani
published in: Journal of Mathematical Economics
publication date: 1999-09-01T00:00:00Z
review text: The interest in this paper is in the system stability of the dynamic processes with multiple equilibria. Utilizing a no-cycle condition of \textit{J. S. Muldowney} [Rocky Mt. J. Math. 20, No. 4, 857-872 (1990; Zbl 0725.34049)] we derive two sufficient conditions for system stability, which provide generalizations of the dominant diagonal conditions with weights. The derived system stability conditions are, therefore, independent of adjustment coefficients. Our system stability conditions are applicable to various types of dynamic adjustment processes. We prove some properties concerning local stability and the number of stable equilibria. We also prove that almost any dynamical system which satisfies our system stability condition is Morse-Smale and, therefore, structurally stable.
Mathematics Subject Classification ID: 91B60
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 37N40
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 1330494
zbMATH Keywords: system stability
zbMATH Keywords: no-cycle conditions
zbMATH Keywords: dominant diagonal conditions with weights
zbMATH Keywords: Pugh's closing lemma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1330494