A Mathematical Modeling Approach From Nonlinear Dynamics To Complex Systems
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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems
This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.
Methods of Mathematical Modelling and Computation for Complex Systems
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.
Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.