Nonlinear Dynamics, Chaos, and Complexity, 1st ed. 2021 In Memory of Professor Valentin Afraimovich Nonlinear Physical Science Series

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 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). 

Chapter 1. Professor Valentin Afraimovich by Alexandra Afraimovich

Chapter 2.The need for more integration between machine learning and neuroscience by   Adrian Hernandez, Jose M. Amigo

Chapter 3.Quasiperiodic Route to Transient Chaos in Vibroimpact System by Victor Bazhenov, Olga Pogorelova, Tatiana Postnikova

Chapter 4. Modeling Ensembles of Nonlinear Dynamic Systems in Ultrawideb and Active Wireless Direct Chaotic Networks by A.S. Dmitriev, R.Yu. Yemelyanov, M.Yu. Gerasimov, Yu.V. Andreyev

Chapter 5.Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species by Messoud Efendiev, Vitali Vougalter

Chapter6.Chaos-based communication using isochronal synchronization:  considerations about the synchronization manifold byJ.M.V.  Grzybowski, E.E.N.  Macau, T.  Yoneyama

Chapter 8.On the Geometric Approach to Transformations of the Coordinates of Inertial Frames of Reference by A.A. Talyshev

Chapter 9.Corpuscular models of information transfer in a random environment by V.V.  Uchaikin

Chapter 10. Kinetic equation for systems with resonant captures and scatterings by A.V.  Artemyev, A.I.  Neishtadt, A.A.  Vasiliev

Chapter 11. Solvability In The Sense Of Sequences  For  Some Non-Fredholm  Operators  In  Higher  Dimensions by Vitali  Vougalter,  Vitaly  Volpert

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