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Qualitative Analysis of Set-Valued Differential Equations

Autor Anatoly A. Martynyuk
en Limba Engleză Hardback – 10 apr 2019
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them.  The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities,  which are used to establish existence, stability or boundedness.
Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.

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Specificații

ISBN-13: 9783030076436
ISBN-10: 3030076431
Pagini: 228
Ilustrații: XIII, 198 p. 1 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.48 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Birkhäuser
Locul publicării:Cham, Switzerland

Cuprins

General Properties of Set Equations.- Analysis of the Set of Continuous Equations.- Stability of the Set of Discrete–Time Systems.- Qualitative Analysis of Set Impulsive Equations.- Stability of Set Systems with Aftereffect.- Analysis of Set Impulsive Systems with Aftereffect.- Stability of Set Equations with Causal Operator.- Finite-Time Stability of Standard Systems Sets

Textul de pe ultima copertă

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them.  The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.

Caracteristici

First book on the theoretical foundations of modeling real-world phenomena by a set of differential equations Focusses on differential equations with uncertainty Written for the experts working in the ?eld of qualitative analysis of di?erential and other types of equations