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Title: Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces
Authors: Awrejcewicz, Jan
Losyeva, Nataliya
Puzyrov, Volodymyr
Keywords: stability
non-conservative system
uncertain parameters
eigenvalue problem
Issue Date: 23-Jul-2020
Publisher: Symmetry 2020
Abstract: 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
Appears in Collections:ННІ природничо-математичних, медико-біологічних наук та інформаційних технологій

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