This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design proc...
"SCIENCE JOURNALISM AT ITS BEST. . . An impeccably researched, amazingly up-to-date, crisply written and well-illustrated survey." --Nature At the cutting edge of the sciences, a dynamic new concept is emerging: complexity. In this groundbreaking new book, Peter Coveney and Roger Highfield explore how complexity in mathematics, physics, biology, chemistry, and even the social sciences is transforming not only the way we think about the universe, but also the very assumptions that underlie conven...
How could a band of physicists in sandals and "Eat the Rich" T-shirts hope to take on the leading lights of high finance? They had never even read the "Journal". But they did know that global finance is an irrational, complex system bordering on chaos. Since two of them, Doyne Farmer and Norman Packard, happened to be among the founders of the new science of chaos and complexity, perhaps they could give it a try. Now, several years - and many millions of dollars - later, they continue one of the...
Caustic Light in Nonlinear Photonic Media (Springer Theses)
by Alessandro Zannotti
Caustics are natural phenomena, forming light patterns in rainbows or through drinking glasses, and creating light networks at the bottom of swimming pools. Only in recent years have scientists started to artificially create simple caustics with laser light. However, these realizations have already contributed to progress in advanced imaging, lithography, and micro-manipulation. In this book, Alessandro Zannotti pioneers caustics in many ways, establishing the field of artificial caustic optic...
This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are co...
Combinatorial Dynamics And Entropy In Dimension One (2nd Edition) (Advanced Series in Nonlinear Dynamics, #5)
by Luis Alseda, Jaume Llibre, and Michal Misiurewicz
This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complex...
Chaos, Complexity and Leadership 2016 (Springer Proceedings in Complexity)
This book covers the proceedings from the 2016 International Symposium on Chaos, Complexity and Leadership, and reflects current research results of chaos and complexity studies and their applications in various fields. Included are research papers in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of chaos and complex systems. Also discussed are leadership and management applications of chaos and complexity theory.
Many complex systems - from immensely complicated ecosystems to minute assemblages of molecules - surprise us with their simple behaviour. Consider, for instance, the snowflake, in which a great number of water molecules arrange themselves in patterns with six-way symmetry. How is it that molecules moving seemingly at random become organized according to the simple, six-fold rule? How do the comings, goings, meetings and eatings of individual animals add up to the simple dynamics of ecosystem po...
Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relati...
This text contains a survey of theories describing the evolution of random waves in nonlinear dispersive media. The three kinds of problems are considered. The first is the investigation of the evolution of initially random waves in nonlinear media describing the integrable and nearly integrable systems. It is important for many branches of acoustics and nonlinear optics, in particular for soliton transmissions in long optical communication systems. The second is the nonlinear waves propagation...
The basic procedures for designing and analysing electronic systems are based largely on the assumptions of linear behavior of the system. Nonlinearities inherent in all real applications very often cause unexpected and even strange behavior. This book presents an electronic engineer's perspective on chaos and complex behavior. It starts from basic mathematical notions which enable understanding of the observed phenomena, and guides the reader through the methodology and tools used in the labora...
Patterns in the Sand (Frontiers in science)
by Terry Bossomaier and David Green
A new vision of the most revolutionary scientific breakthrough of the twentieth century, and beyond.. In this fresh look at the science of complexity, a biologist and a computer scientist discuss this profound new field of knowledge, using examples from starfish to traveling salesmen, from car crashes to the workings of the brain. }Until recently, science has made progress by breaking large systems down into smaller and simpler parts, studying and explaining how these parts operate, and putting...
For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original C...
Thermodynamics and Physical Reality
by Ed Gerck and Edgardo Vogel Gerck
The Elements of Thinking in Systems (The Systems Thinker, #4)
by Albert Rutherford
What do traffic jams, stock market crashes, and wars have in common? They are all explained by complexity, an unsolved scientific puzzle which is considered by many to be the 'Science of Sciences'. In "Two's Company, Three is Complexity", Neil Johnson uses real-life examples as he leads us on a fascinating and entertaining romp through cutting-edge topics like chaos, game theory, economics, and even jazz and quantum physics. From pubs to plants, Johnson shows the surprising ways in which order e...
Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive descript...
Cellular computing is a natural information processing paradigm, capable of modeling various biological, physical and social phenomena, as well as other kinds of complex adaptive systems. The programming of a cellular computer is in many respects similar to the genetic evolution in biology, the result being a proper cell design and a task-specific gene.How should one "program" the cell of a cellular computer such that a dynamic behavior with computational relevance will emerge? What are the "rul...
Strange Nonchaotic Attractors
by Arkady S Pikovsky, Ulrike Feudel, and Sergey P Kuznetsov
Photoinduced Phase Transitions
A new class of insulating solids was recently discovered. When irradiated by a few visible photons, these solids give rise to a macroscopic excited domain that has new structural and electronic orders quite different from the starting ground state. This occurrence is called “photoinduced phase transition”, and this multi-authored book reviews recent theoretical and experimental studies of this new phenomenon.Why and how do photoexcited few electrons finally result in an excited domain with a mac...
Noisy Oscillator, The: The First Hundred Years, From Einstein Until Now
by Moshe Gitterman
This book contains comprehensive descriptions of stochastic processes described by underdamped and overdamped oscillator equations with additive and multiplicative random forcing. The latter is associated with random frequency or random damping. The coverage includes descriptions of various new phenomena discovered in the last hundred years since the explanation of Brownian motion by Einstein, Smoluchovski and Langevin, such as the shift of stable points, noise-enhanced stability, stochastic res...
Aha..... That Is Interesting!: John Holland, 85 Years Young (Exploring Complexity, #1)
by Jan Wouter Vasbinder
John Holland is one of the few scientists, who all by themselves and by their pursuits, helped change the course of science and the wealth of human knowledge. There is hardly a field of science or problems, that is not affected by John's work on complexity and in particular, complex adaptive systems. On the occasion of his 85th birthday, many of his friends wrote about John, about facets of this remarkable man that only people close to him can know and tell.This book collects those stories highl...
Atlas Of Physarum Computing
The slime mould Physarum polycephalum is a large cell visible by the unaided eye. It behaves as an intelligent nonlinear spatially extended active medium encapsulated in an elastic membrane. The cell optimises its growth patterns in configurations of attractants and repellents. This behaviour is interpreted as computation. Numerous prototypes of slime mould computers were designed to solve problems of computational geometry, graphs and transport networks and to implement universal computing circ...
In this book we describe the evolution of Classical Mechanics from Newton's laws via Lagrange's and Hamilton's theories with strong emphasis on integrability versus chaotic behavior.In the second edition of the book we have added historical remarks and references to historical sources important in the evolution of classical mechanics.