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Introduction to modern dynamics : chaos, networks, space and time /
The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
[2015]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Preface; Acknowledgments; Contents; Part 1 Geometric Mechanics; 1 Physics and Geometry; 1.1 Newton and geometry; 1.2 State space and flows; 1.3 Coordinate transformations; 1.4 Non-inertial transformations; 1.5 Uniformly rotating frames; 1.6 Rigid-body motion; 1.7 Summary; 1.8 Bibliography; 1.9 Homework exercises; 2 Hamiltonian Dynamics and Phase Space; 2.1 Hamilton's principle; 2.2 Conservation laws; 2.3 The Hamiltonian function; 2.4 Central force motion; 2.5 Phase space; 2.6 Integrable systems and action-angle variables; 2.7 Summary; 2.8 Bibliography; 2.9 Homework exercises.
- Part 2 Nonlinear Dynamics3 Nonlinear Dynamics and Chaos; 3.1 One-variable dynamical systems; 3.2 Two-variable dynamical systems; 3.3 Discrete iterative maps; 3.4 Three-dimensional state space and chaos; 3.5 Fractals and strange attractors; 3.6 Hamiltonian chaos; 3.7 Summary and glossary; 3.8 Bibliography; 3.9 Homework exercises; 4 Coupled Oscillators and Synchronization; 4.1 Coupled linear oscillators; 4.2 Simple models of synchronization; 4.3 External synchronization of an autonomous phase oscillator; 4.4 External synchronization of a van der Pol oscillator.
- 4.5 Mutual synchronization of two autonomous oscillators4.6 Summary; 4.7 Bibliography; 4.8 Homework exercises; 5 Network Dynamics; 5.1 Network structures; 5.2 Random network topologies; 5.3 Diffusion and epidemics on networks; 5.4 Linear synchronization of identical oscillators; 5.5 Nonlinear synchronization of coupled phase oscillators on regular graphs; 5.6 Summary; 5.7 Bibliography; 5.8 Homework exercises; Part 3 Complex Systems; 6 Neurodynamics and Neural Networks; 6.1 Neuron structure and function; 6.2 Neuron dynamics; 6.3 Network nodes: artificial neurons.
- 6.4 Neural network architectures6.5 Hopfield neural network; 6.6 Content-addressable (associative) memory; 6.7 Summary; 6.8 Bibliography; 6.9 Homework exercises; 7 Evolutionary Dynamics; 7.1 Population dynamics; 7.2 Virus infection and immune deficiency; 7.3 The replicator equation; 7.4 The quasi-species equation; 7.5 The replicator-mutator equation; 7.6 Dynamics of finite numbers (optional); 7.7 Summary; 7.8 Bibliography; 7.9 Homework exercises; 8 Economic Dynamics; 8.1 Micro- and macroeconomics; 8.2 Supply and demand; 8.3 Business cycles; 8.4 Consumer market competition; 8.5 Macroeconomics.
- 8.6 Stochastic dynamics and stock prices (optional)8.7 Summary; 8.8 Bibliography; 8.9 Homework exercises; Part 4 Relativity and Space-Time; 9 Metric Spaces and Geodesic Motion; 9.1 Manifolds and metric tensors; 9.2 Reciprocal spaces in physics; 9.3 Derivative of a tensor; 9.4 Geodesic curves in configuration space; 9.5 Geodesic motion; 9.6 Summary; 9.7 Bibliography; 9.8 Homework exercises; 10 Relativistic Dynamics; 10.1 The special theory; 10.2 Lorentz transformations; 10.3 Metric structure of Minkowski space; 10.4 Relativistic dynamics; 10.5 Linearly accelerating frames (relativistic).