Analysis of the trajectory set of nonlinear dynamics: estimates of solutions and comparison principle
type: Item
instance of: scholarly article
title: Analysis of the trajectory set of nonlinear dynamics: estimates of solutions and comparison principle
zbMATH Open document ID: 1266.34029
DOI: 10.1134/S0012266112100072
author: Yu. A. Martynyuk-Chernienko
author: A. A. Martynyuk
published in: Differential Equations
publication date: 2013-02-15T00:00:00Z
review text: The authors consider families of differential equations of the form \[ D_HX=F(t,X,\alpha),\,\, X(t_0)=X_0\in K_C(\mathbb{R}^n), \] where \(D_HX\) is the Hukuhara derivative, \(F\in C(\mathbb R_+\times K_C(\mathbb R^n)\times S, K_C(\mathbb R^n))\), and \(\alpha\in S\) is a parameter specifying the inaccuracies in the family of differential equations. They obtain estimates for solutions and establish a comparison principle on the basis of an auxiliary matrix-valued Lyapunov function. These results can be used to derive sufficient conditions for the existence properties of trajectories with special properties, including boundedness, practical stability, stability with respect to two measures, structural stability, etc.
reviewed by: Andrej V. Plotnikov
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 6136682
zbMATH Keywords: set differential equation
zbMATH Keywords: Hukuhara derivative
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov function
MaRDI profile type: Publication
cites work: Q3397700
cites work: About the global existence of solutions of a set of differential equations
cites work: Integrals of set-valued functions
cites work: Q5537993
full work available at URL: s0012266112100072
OpenAlex ID: W1977120357
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description: scientific article; zbMATH DE number 6136682