Stability Theory for Dynamic Equations on Time Scales

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Mathematical Analysis
Cover of the book Stability Theory for Dynamic Equations on Time Scales by Anatoly A. Martynyuk, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Anatoly A. Martynyuk ISBN: 9783319422138
Publisher: Springer International Publishing Publication: September 22, 2016
Imprint: Birkhäuser Language: English
Author: Anatoly A. Martynyuk
ISBN: 9783319422138
Publisher: Springer International Publishing
Publication: September 22, 2016
Imprint: Birkhäuser
Language: English

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.

In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. 

In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”

Mathematical analysis on time scales accomplishes exactly this. 

This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.

In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. 

In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”

Mathematical analysis on time scales accomplishes exactly this. 

This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

More books from Springer International Publishing

Cover of the book Introduction to Molecular Vaccinology by Anatoly A. Martynyuk
Cover of the book Doubt-Free Uncertainty In Measurement by Anatoly A. Martynyuk
Cover of the book Understanding Policy Decisions by Anatoly A. Martynyuk
Cover of the book Sertoli Cell Metabolism and Spermatogenesis by Anatoly A. Martynyuk
Cover of the book User-Centric Technology Design for Nonprofit and Civic Engagements by Anatoly A. Martynyuk
Cover of the book Modeling Cellular Systems by Anatoly A. Martynyuk
Cover of the book IGFS 2014 by Anatoly A. Martynyuk
Cover of the book Cyber Resilience of Systems and Networks by Anatoly A. Martynyuk
Cover of the book An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields by Anatoly A. Martynyuk
Cover of the book A Differential Approach to Geometry by Anatoly A. Martynyuk
Cover of the book Life Cycle Assessment in the Agri-food Sector by Anatoly A. Martynyuk
Cover of the book The Genetics and Development of Scoliosis by Anatoly A. Martynyuk
Cover of the book Service Life and Durability of Reinforced Concrete Structures by Anatoly A. Martynyuk
Cover of the book Mechanical Ventilation in the Critically Ill Obese Patient by Anatoly A. Martynyuk
Cover of the book The 'Sailor Prince' in the Age of Empire by Anatoly A. Martynyuk
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy