Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces

Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces

We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are discussed and illus...

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Main Authors: Jan Awrejcewicz, Nataliya Losyeva, Volodymyr Puzyrov
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Symmetry
Subjects:
stability
non-conservative system
uncertain parameters
eigenvalue problem
boundedness
Online Access:https://www.mdpi.com/2073-8994/12/8/1210
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spelling doaj-57c68175e377479ba2fcd63c9c6bd7852020-11-25T02:48:06ZengMDPI AGSymmetry2073-89942020-07-01121210121010.3390/sym12081210Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory ForcesJan Awrejcewicz0Nataliya Losyeva1Volodymyr Puzyrov2Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 90-924 Lodz, PolandDepartment of Mathematics, Faculty of Physics and Mathematics, Sumy State Pedagogical University named after A.S. Makarenko, 40002 Sumy, UkraineDepartment of Mathematics, Faculty of Physics and Mathematics, Sumy State Pedagogical University named after A.S. Makarenko, 40002 Sumy, UkraineWe consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are discussed and illustrated by examples. The case of multiple eigenvalues also is considered, and sufficient conditions of instability are obtained. Some issues of the dynamics of a nonlinear system with an unstable linear approximation are discussed. The behavior of trajectories in the case of unstable equilibrium is investigated, and an example of the chaotic behavior versus the case of bounded solutions is presented and discussed.https://www.mdpi.com/2073-8994/12/8/1210stabilitynon-conservative systemuncertain parameterseigenvalue problemboundedness
collection DOAJ
language English
format Article
sources DOAJ
author Jan Awrejcewicz
Nataliya Losyeva
Volodymyr Puzyrov
spellingShingle Jan Awrejcewicz
Nataliya Losyeva
Volodymyr Puzyrov
Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
Symmetry
stability
non-conservative system
uncertain parameters
eigenvalue problem
boundedness
author_facet Jan Awrejcewicz
Nataliya Losyeva
Volodymyr Puzyrov
author_sort Jan Awrejcewicz
title Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
title_short Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
title_full Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
title_fullStr Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
title_full_unstemmed Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
title_sort stability and boundedness of the solutions of multi-parameter dynamical systems with circulatory forces
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-07-01
description We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are discussed and illustrated by examples. The case of multiple eigenvalues also is considered, and sufficient conditions of instability are obtained. Some issues of the dynamics of a nonlinear system with an unstable linear approximation are discussed. The behavior of trajectories in the case of unstable equilibrium is investigated, and an example of the chaotic behavior versus the case of bounded solutions is presented and discussed.
topic stability
non-conservative system
uncertain parameters
eigenvalue problem
boundedness
url https://www.mdpi.com/2073-8994/12/8/1210
work_keys_str_mv AT janawrejcewicz stabilityandboundednessofthesolutionsofmultiparameterdynamicalsystemswithcirculatoryforces
AT nataliyalosyeva stabilityandboundednessofthesolutionsofmultiparameterdynamicalsystemswithcirculatoryforces
AT volodymyrpuzyrov stabilityandboundednessofthesolutionsofmultiparameterdynamicalsystemswithcirculatoryforces
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