000 05553nam a2200709 i 4500
001 9780750335072
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006 m eo d
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008 210901s2021 enka fob 000 0 eng d
020 _a9780750335072
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020 _a9780750335065
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020 _z9780750335058
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024 7 _a10.1088/978-0-7503-3507-2
_2doi
035 _a(CaBNVSL)thg00082584
035 _a(OCoLC)1266548340
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQ172.5.C45
_bA454 2021eb
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a003/.857
_223
100 1 _aAkhmet, Marat,
_eauthor.
_970437
245 1 0 _aDomain structured dynamics :
_bunpredictability, chaos, randomness, fractals, differential equations and neural networks /
_cMarat Akhmet.
264 1 _aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
_bIOP Publishing,
_c[2021]
300 _a1 online resource (various pagings) :
_billustrations (some color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _a[IOP release $release]
490 1 _aIOP ebooks. [2021 collection]
500 _a"Version: 202108"--Title page verso.
504 _aIncludes bibliographical references.
505 8 _a3. Domain structured dynamics : theory -- 3.1. Basic definitions and theorems -- 3.2. Hyperbolic chaos -- 3.3. Modular chaos -- 3.4. Abstract fractals -- 3.5. Notes
505 8 _a4. Domain structured dynamics : applications -- 4.1. Theoretical preliminaries -- 4.2. Chaotic finite-dimensional cubes -- 4.3. Similarity through Fatou-Julia iterations -- 4.4. Conservative-progressive growth -- 4.5. Domain structured dynamics in fractals -- 4.6. Notes
505 8 _apart III. Random processes. 5. Randomness with similarity dynamics -- 5.1. The basics of abstract similarity -- 5.2. Unpredictability in Bernoulli schemes -- 5.3. Random unpredictable functions -- 5.4. Unpredictable strings -- 5.5. Abstract similarity chaos in Markov chains -- 5.6. Modular chaos in random processes
505 8 _apart IV. Non-autonomous differential equations. 6. Unpredictability in differential equations -- 6.1. Preliminaries -- 6.2. Strongly unpredictable solutions -- 6.3. Unpredictable solutions -- 6.4. Examples -- 6.5. Notes
505 8 _apart V. Neural networks. 7. Unpredictable oscillations of neural networks -- 7.1. SICNNs with strongly unpredictable oscillations -- 7.2. Inertial neural networks with unpredictable oscillations -- 7.3. Notes.
505 0 _apart I. Introduction. 1. What this book is about -- 1.1. Unpredictability -- 1.2. Domain structured dynamics -- 1.3. Random processes -- 1.4. Abstract fractals -- 1.5. Differential equations -- 1.6. Neural networks
505 8 _apart II. Chaos and fractals. 2. Unpredictability implies chaos -- 2.1. Unpredictability in dynamics -- 2.2. Unpredictable functions -- 2.3. Notes
520 3 _aDomain structured dynamics introduces a way for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract similarity dynamics. Then a labeling procedure is designed to determine the domain structured dynamics. The results follow the Pythagorean doctrine, considering finite number of indices for the labeling, with potential to become universal in future. The immediate power of the approach for fractals as domains of chaos, revisited famous deterministic and stochastic models, new types of differential equations and neural networks is seen in the book. This is not considered through widening areas, where the notions can be seen and recognized, but by deepening abstraction.
521 _aSpecialists in nonlinear dynamics, differential and discrete equations, chaos theory, fractal geometry and applications. Engineers, experts in industrial development of all kinds: electronics, chemistry, mechanics, control and optimization.
530 _aAlso available in print.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 _aDr. Marat Akhmet is currently a Professor at Department of Mathematics, METU, Ankara, Turkey. He received his PhD in differential equations and mathematical physics at Kiev State University, Ukraine. Marat Akhmet's research focuses on the dynamical models and differential equations. He has published seven books and more than a hundred and fifty scientific papers. In the last several years, he has been investigating dynamics of neural networks, periodic, almost periodic and unpredictable motions, stability, chaos, and fractals.
588 0 _aTitle from PDF title page (viewed on September 1, 2021).
650 0 _aChaotic behavior in systems.
_94594
650 0 _aDynamics.
_970438
650 0 _aNonlinear theories.
_93339
650 0 _aDifference equations.
_915445
650 0 _aFractals.
_910012
650 7 _aMathematical physics.
_2bicssc
_911013
650 7 _aMathematics and computation.
_2bisacsh
_970439
710 2 _aInstitute of Physics (Great Britain),
_epublisher.
_911622
776 0 8 _iPrint version:
_z9780750335058
_z9780750335089
830 0 _aIOP (Series).
_pRelease 21.
_970440
830 0 _aIOP ebooks.
_p2021 collection.
_970441
856 4 0 _uhttps://iopscience.iop.org/book/978-0-7503-3507-2
942 _cEBK
999 _c82838
_d82838