Synergetic Phenomena in Active Lattices (häftad)
Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
359
Utgivningsdatum
2012-08-17
Upplaga
Softcover reprint of the original 1st ed. 2002
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Medarbetare
Velarde, M. G.
Illustrationer
XVII, 359 p.
Dimensioner
234 x 156 x 20 mm
Vikt
531 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783642627255
Synergetic Phenomena in Active Lattices (häftad)

Synergetic Phenomena in Active Lattices

Patterns, Waves, Solitons, Chaos

Häftad Engelska, 2012-08-17
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In this book, the authors deal with basic concepts and models, with methodologies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition between order and chaos is crucial for synergetic behavior and evolution.
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"The book may serve as an invaluable guide to all those interested in the rich phenomenology of spatio-temporal dynamic phenomena in active lattices, providing the reader with a variety of analytical and numerical methods that can be used in the study of concrete applications. In sum, it is a highly enjoyable, well-written book by two leading scientists in the field, with carefully chosen material, which is highly recommended to anyone wanting a good introduction to the subject." (Mathematical Reviews 2003b) "In an applied, descriptive manner, the authors present and corroborate results through a mixture of heuristics, numerical investigations and mathematical analysis guided by general methods from geometric dynamical systems theory. [...] Each of the well written chapters starts with a motivation and ends with a summary; general conclusions and perspectives are given in the final chapter. [...] This book provides an easily accessible introduction and overview of phenomena and the current state of understanding in the field of waves and synchronization in spatially discrete systems." (Zentralblatt MATH, 1006, 2003) "This book gives a comprehensive account of synergetic phenomena in active lattices. ... throughout the book insights on the possible use of the results in applications such as computer architecture or neuronal science are given. ... The book may serve as an invaluable guide to all those interested in the rich pheonomenology of spatio-temporal dynamic phenomena in active lattices ... . In sum, it is a highly enjoyable, well-written book ... which is highly recommended to anyone wanting a good introduction to the subject." (Athanasios Yannacopoulos, Mathematical Reviews, Issue 2003 b) "The present textbook concerns pattern formation in lattices of coupled cells with oscillatory or excitable dynamics. In an applied, descriptive manner, the authors present and corroborate results through a mixture of heuristics, numerical investigations and mathematical analysis guided by general methods from geometric dynamical systems theory. ... This book provides an easily accessible introduction and overview of phenomena and the current state of understanding in the field of waves and synchronization in spatially discrete systems." (Jens Rademacher, Zentralblatt MATH, Vol. 1006, 2003)

Innehållsförteckning

1. Introduction: Synergetics and Models of Continuous and Discrete Active Media. Steady States and Basic Motions (Waves, Dissipative Solitons, etc.).- 1.1 Basic Concepts, Phenomena and Context.- 1.2 Continuous Models.- 1.3 Chain and Lattice Models with Continuous Time.- 1.4 Chain and Lattice Models with Discrete Time.- 2. Solitary Waves, Bound Soliton States and Chaotic Soliton Trains in a Dissipative Boussinesq-Korteweg-de Vries Equation.- 2.1 Introduction and Motivation.- 2.2 Model Equation.- 2.3 Traveling Waves.- 2.3.1 Steady States.- 2.3.2 Lyapunov Functions.- 2.4 Homoclinic Orbits. Phase-Space Analysis.- 2.4.1 Invariant Subspaces.- 2.4.2 Auxiliary Systems.- 2.4.3 Construction of Regions Confining the Unstable and Stable Manifolds Wu and Ws.- 2.5 Multiloop Homoclinic Orbits and Soliton-Bound States.- 2.5.1 Existence of Multiloop Homoclinic Orbits.- 2.5.2 Solitonic Waves, Soliton-Bound States and Chaotic Soliton-Trains.- 2.5.3 Homoclinic Orbits and Soliton-Trains. Some Numerical Results.- 2.6 Further Numerical Results and Computer Experiments.- 2.6.1 Evolutionary Features.- 2.6.2 Numerical Collision Experiments.- 2.7 Salient Features of Dissipative Solitons.- 3. Self-Organization in a Long Josephson Junction.- 3.1 Introduction and Motivation.- 3.2 The Perturbed Sine-Gordon Equation.- 3.3 Bifurcation Diagram of Homoclinic Trajectories.- 3.4 Current-Voltage Characteristics of Long Josephson Junctions 54.- 3.5 Bifurcation Diagram in the Neighborhood of c = 1.- 3.5.1 Spiral-Like Bifurcation Structures.- 3.5.2 Heteroclinic Contours.- 3.5.3 The Neighborhood of Ai.- 3.5.4 The Sets {?i} and {?i}.- 3.6 Existence of Homoclinic Orbits.- 3.6.1 Lyapunov Function.- 3.6.2 The Vector Field of (3.4) on Two Auxiliary Surfaces.- 3.6.3 Auxiliary Systems.- 3.6.4 "Tunnels" for Manifolds of the Saddle Steady State O2.- 3.6.5 Homoclinic Orbits.- 3.7 Salient Features of the Perturbed Sine-Gordon Equation.- 4. Spatial Structures, Wave Fronts, Periodic Waves, Pulses and Solitary Waves in a One-Dimensional Array of Chua's Circuits.- 4.1 Introduction and Motivation.- 4.2 Spatio-Temporal Dynamics of an Array of Resistively Coupled Units.- 4.2.1 Steady States and Spatial Structures.- 4.2.2 Wave Fronts in a Gradient Approximation.- 4.2.3 Pulses, Fronts and Chaotic Wave Trains.- 4.3 Spatio-Temporal Dynamics of Arrays with Inductively Coupled Units.- 4.3.1 Homoclinic Orbits and Solitary Waves.- 4.3.2 Periodic Waves in a Circular Array.- 4.4 Chaotic Attractors and Waves in a One-Dimensional Array of Modified Chua's Circuits.- 4.4.1 Modified Chua's Circuit.- 4.4.2 One-Dimensional Array.- 4.4.3 Chaotic Attractors.- 4.5 Salient Features of Chua's Circuit in a Lattice.- 4.5.1 Array with Resistive Coupling.- 4.5.2 Array with Inductive Coupling.- 5. Patterns, Spatial Disorder and Waves in a Dynamical Lattice of Bistable Units.- 5.1 Introduction and Motivation.- 5.2 Spatial Disorder in a Linear Chain of Coupled Bistable Units.- 5.2.1 Evolution of Amplitudes and Phases of the Oscillations.- 5.2.2 Spatial Distributions of Oscillation Amplitudes.- 5.2.3 Phase Clusters in a Chain of Isochronous Oscillators.- 5.3 Clustering and Phase Resetting in a Chain of Bistable Nonisochronous Oscillators.- 5.3.1 Amplitude Distribution along the Chain.- 5.3.2 Phase Clusters in a Chain of Nonisochronous Oscillators.- 5.3.3 Frequency Clusters and Phase Resetting.- 5.4 Clusters in an Assembly of Globally Coupled Bistable Oscillators.- 5.4.1 Homogeneous Oscillations.- 5.4.2 Amplitude Clusters.- 5.4.3 Amplitude-Phase Clusters.- 5.4.4 "Splay-Phase" States.- 5.4.5 Collective Chaos.- 5.5 Spatial Disorder and Waves in a Circular Chain of Bistable Units.- 5.5.1 Spatial Disorder.- 5.5.2 Space-Homogeneous Phase Waves.- 5.5.3 Space-Inhomogeneous Phase Waves.- 5.6 Chaotic and Regular Patterns in Two-Dimensional Lattices of Coupled Bistable Units.- 5.6.1 Methodology for a Lattice of Bistable Elements.- 5.6.2 Stable Steady States.- 5.6.3 Spatial Disorder and Patterns in the Fitz