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Nonlinear Dynamics, Chaos, and Complexity

In Memory of Professor Valentin Afraimovich

  • Book
  • © 2021

Overview

Editors:
  1. Dimitri Volchenkov

    1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA

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  • Presents recent advances in discontinuous and nonlinear dynamical systems, chaos, and complexity science
  • Develops the corresponding mathematical theory to apply nonlinear design to practical engineering
  • Provides methods for mathematical models with switching, thresholds, and impulses
  • Represents a new step into the understanding of complex dynamical systems and the relation between their structure and functions

Part of the book series: Nonlinear Physical Science (NPS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Professor Valentin Afraimovich

    • Alexandra Afraimovich
    Pages 1-8

  3. The Need for More Integration Between Machine Learning and Neuroscience

    • Adrián Hernández, José M. Amigó
    Pages 9-19

  4. Quasiperiodic Route to Transient Chaos in Vibroimpact System

    • Victor Bazhenov, Olga Pogorelova, Tatiana Postnikova
    Pages 21-46

  5. Modeling Ensembles of Nonlinear Dynamic Systems in Ultrawideband Active Wireless Direct Chaotic Networks

    • A. S. Dmitriev, R. Yu. Yemelyanov, M. Yu. Gerasimov, Yu. V. Andreyev
    Pages 47-63

  6. Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species

    • Messoud Efendiev, Vitali Vougalter
    Pages 65-74

  7. Chaos-Based Communication Using Isochronal Synchronization: Considerations About the Synchronization Manifold

    • J. M. V. Grzybowski, E. E. N. Macau, T. Yoneyama
    Pages 75-94

  8. A Sequential Order of Periodic Motions in a 1-Dimensional, Time-Delay, Dynamical System

    • Siyuan Xing, Albert C. J. Luo
    Pages 95-112

  9. On the Geometric Approach to Transformations of the Coordinates of Inertial Frames of Reference

    • A. A. Talyshev
    Pages 113-124

  10. Corpuscular Models of Information Transfer in a Random Environment

    • V. V. Uchaikin
    Pages 125-170

  11. Kinetic Equation for Systems with Resonant Captures and Scatterings

    • A. V. Artemyev, A. I. Neishtadt, A. A. Vasiliev
    Pages 171-180

  12. Solvability in the Sense of Sequences for Some Non-Fredholm Operators in Higher Dimensions

    • Vitali Vougalter, Vitaly Volpert
    Pages 181-198
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Keywords

About this book

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. 

The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. 

The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background). 



Editors and Affiliations

  • Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA

    Dimitri Volchenkov

About the editor

Dr. Dimitri Volchenkov obtained his Ph.D. in Theoretical Physics in the Saint Petersburg State University (Russia) and habilitated in the CNRS Centre de Physique Theorique (Marseille, France). He is the Associate Professor of Mathematics and Statistics at the Texas Tech University (USA) and Professor of Risk Assessment and Data Science at the Sichuan University of Science and Engineering (China). His research interests are the science of complexity and interdisciplinary physics ranging from the stochastic nonlinear dynamics, to plasma turbulence, to urban spatial networks, and their impact on poverty and environments, analysis of complex networks, data analysis of economic, inequality and politics data, big data analytics, survival analysis, and modelling of evolutionary biology and ecology.

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