The Many Facets of Complexity Science, 1st ed. 2021 In Memory of Professor Valentin Afraimovich Nonlinear Physical Science Series

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely

Entropy, information, and complexity functions

Multistability, oscillations, and rhythmic synchronization

Diffusions, rotation, and convection in fluids

The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics.

The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.

Chapter 1. Maurice Courbage: The Directional Entropy for Spatially Extended Dynamical Systems

Chapter 2. Olivier Bui, Xavier Leoncini, Detecting Regularity with Complexity Functions
Chapter 3. Raul Rechtman, Local Complexity Functions of the Ehrenfest’s wind-tree model

Chapter 4.Bastien Fernandez, Selective Chaos of Travelling Waves in Feedforward Chains of Bistable Maps

Chapter 5. Yeyin Xu, Albert C.J. Luo, On Periodic Motions in a van der Pol Oscillator

Chapter 6. Jianzhe Huang, Fuhong Min , Hidden periodic motions for brushless motor with unsteady torque excitation

Chapter 7. Stefano Boccaletti, H. Bi, T. Qui, I. Bonamassa, Shuguang Guan, Chunking Rhythmic Synchronization: Bellerophon States and Quantized Clusters of Globally Coupled Phase Oscillators

Chapter 8. Shasha Zheng, Xilin Fu, Chatter Dynamics and Stability of the Impulsive van der Pol Equation

Chapter 9. Xilin Fu, Yanyan Zhang, Complex Motions in an Inclined Impact Pair With a Periodic Excitation

Chapter 10. Dmitry V. Kovalevsky, Igor L. Bashmachnikov:Nonlinear Dynamics of Deep Open-Ocean Convection: An Analytical Approach

Chapter 11.  Messoud  Efendiev, Vitali  Vougalter: On the Necessary Conditions for Preserving the Nonnegative Cone: Mixed Diffusion

Chapter 12. Dimitri Volchenkov，Veniamin Smirnov:Multi-scale Analysis of Urban Spatial Structures acquired from OpenStreetMap

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 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, 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.

Represents the new step into our understanding of complexity science

Develops the corresponding mathematical theory to apply nonlinear design to practical engineering

Covers physical problems and mathematical modelling