Download or read book Theory and Applications of Coupled Map Lattices written by K. Kaneko and published by . This book was released on 1993-04-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The technique of the coupled map lattice (CML) is a rapidly developing field in nonlinear dynamics at present. This book gives a fully illustrative overview of current research in the field. A CML is a dynamical system in which there is some interaction ('coupled') between continuous state elements, which evolve in discrete time ('map') and are distributed on a discrete space ('lattice'). This book investigates both the theoretical aspects and applications of CMLs to spatially extended systems in nonlinear dynamical systems.
Download or read book Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems written by Jean-René Chazottes and published by Springer Science & Business Media. This book was released on 2005-07-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.
Download or read book Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems written by Jean-René Chazottes and published by Springer. This book was released on 2009-09-02 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.
Download or read book From Finite to Infinite Dimensional Dynamical Systems written by James Robinson and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six papers originally presented at a NATO Advanced Study Institute held in Cambridge, U.K. in 1995 on the fundamental properties of partial differential equations and modeling processes involving spatial dynamics. The contributors, from academic institutions in Europe and the U.S., discuss such topics as lattice dynamical systems, low-dimensional models of turbulence, and nonlinear dynamics of extended systems. The volume is not indexed. c. Book News Inc.
Download or read book Animal Space Use Second Edition written by Arild O. Gautestad and published by Cambridge Scholars Publishing. This book was released on 2021-08-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Animal space use is complex, from both the individual and population perspectives. Spatial memory leads to site fidelity, the emergence of home ranges, and multi-scaled use of the environment. Attraction to conspecifics—another memory-dependent property—contributes to population survival by counteracting decline in local abundance from unconstrained dispersal. However, memory effects, multi-scaled space use, and intra-specific cohesion present deep theoretical challenges for biophysical modelling. This book confronts these issues straight on, and presents a range of novel system descriptors, model designs, and simulations; intrinsic properties from memory and scaling are illustrated in detail, and classical models are scrutinized with respect to compliance with real data. The presentations of concepts are geared towards a broad audience of researchers and students with an interest in animal space use. The book advocates that an extension of the biophysical frame of reference may be needed to understand systems that express intrinsic complexity from the combined effects of scaling and memory. It boldly provides an overview and critical evaluation of existing concepts, and a wide range of theoretical proposals to resolve present challenges.
Download or read book Instabilities Chaos And Turbulence 2nd Edition written by Paul Manneville and published by World Scientific. This book was released on 2010-07-21 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation./a
Download or read book Instabilities Chaos and Turbulence written by Paul Manneville and published by World Scientific. This book was released on 2010 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.
Download or read book Formation Dynamics And Statistics Of Patterns Volume 1 written by Onuki Akira and published by World Scientific. This book was released on 1990-01-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Patterns are becoming the focal point of many areas of scientific endeavour in recent years owing to the progress of computer science, laboratory experiments and observations, and analytical tools. This book brings together articles by the leading experts in this field. The following topics are discussed in this volume: current status of pattern research with emphasis on real phenomena and new theoretical concepts; interdisciplinary subjects involving Statistical Physics, Condensed Matter Physics, Fluid Mechanics, Nonequilibrium and Nonlinear Phenomena.
Download or read book Nonlinear System Identification written by Stephen A. Billings and published by John Wiley & Sons. This book was released on 2013-09-23 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
Download or read book Fractal Worlds written by Michael Frame and published by Yale University Press. This book was released on 2016-06-21 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.
Download or read book Topics in Nonlinear Dynamics written by Erik Mosekilde and published by World Scientific. This book was released on 2003-03-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science.
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 1107 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Download or read book String Theory Research Progress written by Ferenc N. Balogh and published by Nova Publishers. This book was released on 2008 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges. Moreover, it may be possible to 'unify' the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory) space-time dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory.
Download or read book Complex Systems Chaos and Beyond written by Kunihiko Kaneko and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.
Download or read book Permutation Complexity in Dynamical Systems written by José Amigó and published by Springer Science & Business Media. This book was released on 2010-03-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.
Download or read book Future Directions of Nonlinear Dynamics in Physical and Biological Systems written by P.L. Christiansen and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early in 1990 a scientific committee was formed for the purpose of organizing a high-level scientific meeting on Future Directions of Nonlinear Dynamics in Physical and Biological Systems, in honor of Alwyn Scott's 60th birthday (December 25, 1991). As preparations for the meeting proceeded, they were met with an unusually broad-scale and high level of enthusiasm on the part of the international nonlinear science community, resulting in a participation by 168 scientists from 23 different countries in the conference, which was held July 23 to August 11992 at the Laboratory of Applied Mathematical Physics and the Center for Modelling, Nonlinear Dynamics and Irreversible Thermodynamics (MIDIT) of the Technical University of Denmark. During the meeting about 50 lectures and 100 posters were presented in 9 working days. The contributions to this present volume have been grouped into the following chapters: 1. Integrability, Solitons, and Coherent Structures 2. Nonlinear Evolution Equations and Diffusive Systems 3. Chaotic and Stochastic Dynamics 4. Classical and Quantum Lattices and Fields 5. Superconductivity and Superconducting Devices 6. Nonlinear Optics 7. Davydov Solitons and Biomolecular Dynamics 8. Biological Systems and Neurophysics. AI Scott has made early and fundamental contributions to many of these different areas of nonlinear science. They form an important subset of the total number of the papers and posters presented at the meeting. Other papers from the meeting are being published in a special issue of Physica D Nonlinear Phenomena.
Download or read book Spatiotemporal Chaos is One and Two dimensional Coupled Map Lattices written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled map lattices are investigated as a model for spatiotemporal chaos. Pattern dynamics in diffusively coupled logistic lattice is briefly reviewed with the use of power spectra, domain distribution, and Lyapunov spectra. Mechanism of pattern selection with the suppression of chaos is discussed. Pattern dynamics on a 2-dimensional lattice is shown. In a weak coupling regime, a similarity with the one-dimensional case is found; frozen random pattern, pattern selection, Brownian motion of a chaotic string, and intermittent collapse of the pattern with selective flicker noise. In a strong coupling regime, frozen pattern is found to be unstable by the surface tension, which is in contrast with the one-dimensional case. Convective coupling model is introduced in connection with the fluid turbulence of Navier--Stokes type. Soliton turbulence and vortex turbulence in the model are reported. Physical implications of coupled map lattices are discussed.
