Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately.
This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the...
Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have be...
Complexity understanding and management will be a main source of efficiency and prosperity for the next decades and thus is of highest industrial and scientific interest. This book on the latest in polystochastic models for complexity includes case studies.
Complexity understanding and management will be a main source of efficiency and prosperity for the next decades and thus is of highest industrial and ...
One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world...
One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evoluti...
Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics - CA have also become work horses in very...
Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for...
Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties are not directly deducible from the lower-level motion of that system. Emergent properties are properties of the "whole'' that are not possessed by any of the individual parts making up that whole. Such phenomena exist in various domains and can be described, using complexity concepts and thematic knowledges. This book highlights complexity modelling through dynamical or behavioral systems. The...
Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dyn...
What are the principles that keep our society together? This question is even more difficult to answer than the long-standing question, what are the forces that keep our world together. However, the social challenges of humanity in the 21st century ranging from the financial crises to the impacts of globalization, require us to make fast progress in our understanding of how society works, and how our future can be managed in a resilient and sustainable way. This book can present only a few very first steps towards this ambitious goal. However, based on simple models of social interactions,...
What are the principles that keep our society together? This question is even more difficult to answer than the long-standing question, what are the f...
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology-and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role. This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they...
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, i...
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped...
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical sys...
This book introduces a refreshing approach to twenty-first-century scientific approach in an age, which is also known as the Century of Complexity. It deals with the deep problem of complexity, being operative from the bottom-up. The current lack of understanding of complexity has led scholars into the so-called embarrassment of complexity. A long overdue paradigm shift is necessary to address complexity as generative complexity and brings readers to the edge of a scientific revolution: that is, a generative revolution in the Century of Complexity.
The book offers a...
This book introduces a refreshing approach to twenty-first-century scientific approach in an age, which is also known as the Century of Complexity....
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants.
The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the...
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced ...
