Domain structured dynamics : unpredictability, chaos, randomness, fractals, differential equations and neural networks /

Domain 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 dom...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Akhmet, Marat (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Chaotic behavior in systems.
Dynamics.
Nonlinear theories.
Difference equations.
Fractals.
Mathematical physics.
Mathematics and computation.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 3. 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
  • 4. 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
  • part 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
  • part 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
  • part 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.
  • part 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
  • part II. Chaos and fractals. 2. Unpredictability implies chaos
  • 2.1. Unpredictability in dynamics
  • 2.2. Unpredictable functions
  • 2.3. Notes

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