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Title
Theory of translation closedness for time scales : with applications in translation functions and dynamic equations / Chao Wang, Ravi P. Agarwal, Donal O' Regan, Rathinasamy Sakthivel.
ISBN
9783030386443 (electronic book)
3030386449 (electronic book)
9783030386436
Publication Details
Cham : Springer, 2020.
Language
English
Description
1 online resource (586 pages).
Item Number
10.1007/978-3-030-38
10.1007/978-3-030-38644-3 doi
Call Number
QA353.P4
Dewey Decimal Classification
515/.39
Summary
This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Bibliography, etc. Note
Includes bibliographical references and index.
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Digital File Characteristics
text file PDF
Source of Description
Description based on print version record.
Series
Developments in mathematics ; v. 62.
Preface
Preliminaries and Basic Knowledge on Time Scales
A Classification of Closedness of Time Scales under Translations
Almost Periodic Functions and Generalizations on Complete-Closed Time Scales
Piecewise Almost Periodic Functions and Generalizations on Translation Time Scales
Almost Automorphic Functions and Generalizations on Translation Time Scales
Nonlinear Dynamic Equations on Translation Time Scales
Impulsive Dynamic Equations on Translation Time Scales
Almost Automorphic Dynamic Equations on Translation Time Scales
Analysis of Dynamical System Models on Translation Time Scales
Index.
