國立虎尾科技大學 |

Almost Periodicity, Chaos, and Asymptotic Equivalence

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Almost Periodicity, Chaos, and Asymptotic Equivalence/ by Marat Akhmet.
作者:	Akhmet, Marat.
面頁冊數:	XVII, 360 p. 26 illus., 25 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical Models of Cognitive Processes and Neural Networks. -
電子資源:	https://doi.org/10.1007/978-3-030-20572-0
ISBN:	9783030205720

Almost Periodicity, Chaos, and Asymptotic Equivalence
Akhmet, Marat.

Almost Periodicity, Chaos, and Asymptotic Equivalence[electronic resource] /by Marat Akhmet. - 1st ed. 2020. - XVII, 360 p. 26 illus., 25 illus. in color.online resource. - Nonlinear Systems and Complexity,272195-9994 ;. - Nonlinear Systems and Complexity,12.

Chapter 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.

The 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.

ISBN: 9783030205720

Standard No.: 10.1007/978-3-030-20572-0doiSubjects--Topical Terms:

884110
Mathematical Models of Cognitive Processes and Neural Networks.

LC Class. No.: TA329-348

Dewey Class. No.: 519

Almost Periodicity, Chaos, and Asymptotic Equivalence
LDR:03889nam a22004095i 4500 001 1017733
003 DE-He213
005 20200703072600.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030205720 $9 978-3-030-20572-0
024 7 $a 10.1007/978-3-030-20572-0 $2 doi
035 $a 978-3-030-20572-0
050 4 $a TA329-348
050 4 $a TA640-643
072 7 $a TBJ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a TBJ $2 thema
082 0 4 $a 519 $2 23
100 1 $a Akhmet, Marat. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 788072
245 1 0 $a Almost Periodicity, Chaos, and Asymptotic Equivalence $h [electronic resource] / $c by Marat Akhmet.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XVII, 360 p. 26 illus., 25 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Nonlinear Systems and Complexity, $x 2195-9994 ; $v 27
505 0 $a Chapter 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 $a The 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 2 4 $a Mathematical Models of Cognitive Processes and Neural Networks. $3 884110
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 1113607
650 1 4 $a Mathematical and Computational Engineering. $3 1139415
650 0 $a Neural networks (Computer science) . $3 1253765
650 0 $a Differential equations. $3 527664
650 0 $a Statistical physics. $3 528048
650 0 $a Engineering mathematics. $3 562757
650 0 $a Applied mathematics. $3 1069907
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030199166
776 0 8 $i Printed edition: $z 9783030206543
830 0 $a Nonlinear Systems and Complexity, $x 2195-9994 ; $v 12 $3 1254402
856 4 0 $u https://doi.org/10.1007/978-3-030-20572-0
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)