Screen LibraryStability, structures, and chaos in nonlinear synchronization networks /
The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This boo...
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| Corporate Authors: | |
|---|---|
| Group Author: | ; ; |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1994. |
| Literature type: | eBook |
| Language: |
English Russian |
| Series: |
World Scientific series on nonlinear science. Series A, Monographs and treatises ;
v. 6 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/2412#t=toc |
| Summary: |
The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences. |
| Carrier Form: | 1 online resource (xii,246pages) : illustrations (some color). |
| Bibliography: | Includes bibliographical references (pages 237-246) |
| ISBN: | 9789812798718 |
| CLC: | TP393 |
| Contents: | 1. Basic models. 1.1. Synchronization in nature and technology. 1.2. Automatic synchronization systems. 1.3. Collective systems. 1.4. Lattice models -- 2. Dynamics of a chain of phase lock-loop systems with unidirectional coupling. 2.1. The equation of a flow chain. Dynamics of a "point" element. 2.2. Synchronization regime. 2.3. Development of spatial instabilities. Landau model of developing turbulence. 2.4. Transition processes -- 3. Effect of inertia of elements on the dynamics of a flow chain. 3.1. Dynamics of a partial system with a filter. 3.2. On possible regimes in the chain. 3.3. Global synchronization. 3.4. Scenarios for the development of chaos. 3.5. Characteristics of transition processes. 3.6. Pattern formation. 3.7. Chains with more complicated dynamics of elements -- 4. Chains with mutual coupling. 4.1. Synchronization in isotropic and anisotropic chains. 4.2. Stationary structures. Chaos. 4.3. Transition processes. 4.4. A chain of coupled inertial systems -- 5. Chains with coupling through phase mismatching signals. 5.1. Flow chain. 5.2. Mutual coupling -- 6. Nonlinear dynamics of lattices. 6.1. Synchronization processes in the lattice with unidirectional coupling. 6.2. Isotropic lattices. 6.3. Coherent periodic structures. 6.4. The influence of the external field on the lattice dynamics -- 7. Analysis of stationary synchronization regimes. 7.1. Stationary regimes in the chain. 7.2. Stationary regimes in the lattice -- 8. Some remarks on other kinds of chains of synchronization systems. 8.1. Series chains. 8.2. Wave properties of the chain of frequency lock loops -- 9. Stability and chaos in the chains of discrete phase-lock loops. 9.1. On the dynamics of a partial system. 9.2. Chaotic and regular chain behavior. 9.3. Conditions of existence of a stable stationary regime. 9.4. Conditions of synchronization -- 10. Dynamics of a ring chain of discrete systems. 10.1. Possibility of synchronization. 10.2. Regular dynamics and chaos in the ring chain. 10.3. Stationary waves and spatially homogeneous regimes. 10.4. Stability of stationary waves. 10.5. Modulated waves -- 11. Order and chaos in the discrete model of an active medium. 11.1. Some remarks on the model. 11.2. Chaotic dynamics of the model. 11.3. Spatially homogeneous and stationary states. 11.4. Stationary waves -- 12. Results and problems. |