Emergence Of Dynamical Order
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Emergence of Dynamical Order
Large populations of interacting active elements, periodic or chaotic, can undergo spontaneous transitions to dynamically ordered states. These collective states are characterized by self-organized coherence revealed by full mutual synchronization of individual dynamics or the formation of multiple synchronous clusters. Such self-organization phenomena are essential for the functioning of complex systems of various origins, both natural and artificial. This book provides a detailed introduction to the theory of collective synchronization phenomena in large complex systems. Transitions to dynamical clustering and synchronized states are systematically discussed. Such concepts as dynamical order parameters, glass like behavior and hierarchical organization are presented.
Order and Chaos in Dynamical Astronomy
Author: George Contopoulos
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
There have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969). But the most complete book in this field is Binney and Tremaine's "Galactic Dynamics" (1987). This book covers well the classical topics of stellar dynamics, and many subjects of current interest. Another classical book in dynamical astronomy is the extensive 4-Volume treatise of Hagihara "Celestial Mechanics" (1970, 1972, 1974, 1975). In more recent years much progress has been made on new topics that are of vital interest for stellar and galactic dynamics. The main new topic is Chaos. The progress of the theory of chaos has influenced considerably the area of stellar and galactic dynamics. The study of order and chaos has provided a new dimension in dynamics.
Discrete Dynamical Systems
Author: Oded Galor
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-05-17
This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.