Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Characteristic Polynomial of an Equlibrium State of an Autonomous System Having an Attracting Invariant Manifold

Author(s):

Alexander V. Bratishchev

Don State Technical University,
Professor of Applied Mathematics Department

avbratishchev@spark-mail.ru

Abstract:

Let an autonomous system have an invariant global attracting in the sense of A. A. Kolesnikov manifold. Then all equilibrium states of the system belong to the set. For each state the explicit form of the eigenvalues of the linearization matrix (in the amount equal to the manifold codimensioin) was found. This allows us to reduce the power of characteristic polynomial and facilitates the study of the topological character of equilibrium. In the particular case of the invariant plane we prove that the above mentioned attracting as a whole is equivalent to global stability

Keywords

• attracting invariant set
• autonomous system
• characteristic polynomial
• eigenvalue
• the state of equilibrium

References:

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