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Domain Structured Dynamics: Unpredictability, Chaos, Randomness, Fractals, Differential Equations and Neural Networks (Iop eBooks) - Hardcover

Akhmet, Marat

 
9780750335058: Domain Structured Dynamics: Unpredictability, Chaos, Randomness, Fractals, Differential Equations and Neural Networks (Iop eBooks)
Hardcover
ISBN 10: 075033505X ISBN 13: 9780750335058
Publisher: Iop Publishing Ltd, 2021

Synopsis

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 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.

Key Features

  • Provides the abstract similarity map, which generalizes the Bernoulli shift for abstract self-similar sets.
  • Discusses dynamically generated self-similar sets as a method of chaos generation.
  • Introduces abstract fractals as sets of metric spaces on the basis of abstract similar sets.
  • Presents fractals concepts discussed through the newly introduced notions.

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About the Author

Dr 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.

"About this title" may belong to another edition of this title.

Publisher
Iop Publishing Ltd
Publication date
2021
Language
English
ISBN 10 
075033505X
ISBN 13 
9780750335058
Binding
Hardcover
Number of pages
150