000 04663nam a22005775i 4500
001 978-3-030-20572-0
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008 190620s2020 sz | s |||| 0|eng d
020 _a9783030205720
_9978-3-030-20572-0
024 7 _a10.1007/978-3-030-20572-0
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620
_223
100 1 _aAkhmet, Marat.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_932909
245 1 0 _aAlmost Periodicity, Chaos, and Asymptotic Equivalence
_h[electronic resource] /
_cby Marat Akhmet.
250 _a1st ed. 2020.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2020.
300 _aXVII, 360 p. 26 illus., 25 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aNonlinear Systems and Complexity,
_x2196-0003 ;
_v27
505 0 _aChapter 1. Introduction -- Chapter 2. Generalities for Impulsive systems -- Chapter 3. Discontinuous Almost Periodic Functions -- Chapter 4. Discontinuos Almost Periodic Solutions -- Chapter 5. Bohr and Bochner Discontinuities -- Chapter 6. Exponentially Dichotomous Linear EPCAG -- Chapter 7. Functional Response on Piecewise Constant Argument -- Chapter 8. SICNN with Functional REsponse on PCA -- Chapter 9. Differential Equations on Time SCales -- Chapter 10. Almost Periodicity in Chaos -- Chapter 11. Homoclinic Chaos and Almost Periodicity -- Chapter 12. SICNN with Chaotic/Almost Periodic Post Synaptic Currents -- Chapter 13. Asymptomatic Equivalence and Almost Periodic Soulutions -- Chapter 14. Asymptomatic Equivalence of Hybrid Systems.
520 _aThe central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aNonlinear Optics.
_911414
650 0 _aDifferential equations.
_932910
650 0 _aNeural networks (Computer science) .
_932911
650 1 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aNonlinear Optics.
_911414
650 2 4 _aDifferential Equations.
_932912
650 2 4 _aMathematical Models of Cognitive Processes and Neural Networks.
_932913
710 2 _aSpringerLink (Online service)
_932914
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030199166
776 0 8 _iPrinted edition:
_z9783030206543
830 0 _aNonlinear Systems and Complexity,
_x2196-0003 ;
_v27
_932915
856 4 0 _uhttps://doi.org/10.1007/978-3-030-20572-0
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c75333
_d75333