Nonlinear Dynamics, Chaos, and Complexity

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).

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

Autorentext

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.

Inhalt

Professor Valentin Afraimovich.- The need for more integration between machine learning and neuroscience. Quasiperiodic Route to Transient Chaos in Vibroimpact System.- Modeling Ensembles of Nonlinear Dynamic Systems in Ultrawideb and Active Wireless Direct Chaotic Networks.- Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species.- Chaos-based communication using isochronal synchronization: considerations about the synchronization manifold.