$Domain Structured Dynamics: Unpredictability, chaos, randomness, fractals, differential equations and neural networks by Professor Marat Akhmet (Middle East Technical University (Turkey)) at Abbey's Bookshop,$

Domain Structured Dynamics: Unpredictability, chaos, randomness, fractals, differential equations and...

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Professor Marat Akhmet (Middle East Technical University (Turkey))

Domain Structured Dynamics

Unpredictability, chaos, randomness, fractals, differential equations and neural networks

Professor Marat Akhmet (Middle East Technical University (Turkey))

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English

Institute of Physics Publishing
04 August 2021

Dynamics & statics; Mathematical physics

Series: IOP ebooks

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.

By: Professor Marat Akhmet (Middle East Technical University (Turkey))
Imprint: Institute of Physics Publishing
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm, Spine: 13mm
ISBN: 9780750335058
ISBN 10: 075033505X
Series: IOP ebooks
Pages: 202
Publication Date: 04 August 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.