Algebraic and radical potential fields. Stability domains in coordinate and parametric space

A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ∈ Rn and parameters A ∈ Rm. We are looking for stability domains in both spaces, i.e. (a) domain P ⊂ Rm such that for any parameter v...

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Bibliographic Details
Main Author: Uteshev, Alexei Yu
Format: Conference Proceeding
Language:English
Online Access:Get full text
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Summary:A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ∈ Rn and parameters A ∈ Rm. We are looking for stability domains in both spaces, i.e. (a) domain P ⊂ Rm such that for any parameter vector specialization A ∈ P, there exists a stable equilibrium for the dynamical system, and (b) domain S ⊂ Rn such that any point X* ∈ S could be made a stable equilibrium by a suitable specialization of the parameter vector A.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5034738