Networks, Games, and Dynamics: From Dynamical Systems and Stochastic Analysis to Transportation Theory and Optimal Control (Trends in Mathematics)

This contributed volume provides an integrated perspective on modern mathematical and computational techniques for addressing complex problems in networks, control systems, learning, and game theory. It encompasses state-of-the-art research from a diverse range of disciplines, including dynamical systems, stochastic analysis, optimization, game theory, machine learning, and transportation theory. Particular emphasis is placed on connecting rigorous theoretical developments with real-world applications.

This volume is organized into twelve chapters. The first part (Chapters 1-6) addresses the optimal transportation problem in traffic networks. The second part (Chapters 7-11) investigates Markov chains with memory by examining the geometric, algebraic, dynamical, and ergodic properties of quadratic (polynomial) stochastic operators associated with cubic stochastic hypermatrices. Finally, Chapter 12 illustrates how methods from stochastic analysis and dynamical systems can be applied to lattice models of statistical mechanics defined on a Cayley tree.

Intended to serve as a comprehensive reference for academics and researchers, this volume may also benefit practitioners and anyone interested in exploring the interplay among these fields.

Mansoor Saburov is an Associate Professor at the Gulf University for Science and Technology. He received his PhD in Mathematics (2011) from the International Islamic University Malasia. His research interests lie in dynamical systems, functional analysis, quantum probability, and (p)-adic analysis.

Naira Hovakimyan is a Professor at the University of Illinois at Urbana-Champaign, USA. She received her PhD in Physics and Mathematics (1992) from the Institute of Applied Mathematics of the Russian Academy of Sciences. Her research interests include control and optimization, autonomous systems, machine learning, neural networks, and their applications.

Armen Badgasaryan is Researcher at the Institute of Mathematics of the National Academy of Sciences, Armenia, and Associate Professor at the Institute of Mathematics and Informatics of Russian-Armenian University, Armenia. He holds a Ph.D. in applied mathematics (2000) from the Russian Academy of Sciences. He does research in the fields of number theory, analysis, dynamical systems, optimization and control, and optimal transport.