Screen LibraryTopics in nonlinear dynamics : applications to physics, biology, and economic systems /
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 th...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1996. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3194#t=toc |
| Summary: |
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. |
| Carrier Form: | 1 online resource (xi,380pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789812819994 |
| CLC: | O175 |
| Contents: | 1. Introduction. 1.1. The new insight. 1.2. Acoustoelectric amplification and subharmonic generation. 1.3. Entrainment of coupled oscillators. 1.4. Anomalous statistics for type-III intermittency. 1.5. Bifurcation structure of two coupled maps -- 2. Deterministic approach to die tossing. 2.1. How random is a die toss? 2.2. The flight and collision maps. 2.3. Distribution of preimages. 2.4. Mixing calculations. 2.5. Dynamics of a loaded die. 2.6. Outcome distribution for the loaded die -- 3. Bifurcation analysis of simple nonlinear systems. 3.1. Duffing's equation and the origin of chaos. 3.2. Collection of steady states. 3.3. Characterizing the chaotic solutions. 3.4. The optical ring cavity. 3.5. The Ikeda map. 3.6. Continuation methods. 3.7. Bifurcation structure for the Ikeda map -- 4. Coupled period-doubling systems. 4.1. Emergence of quasiperiodicity. 4.2. Two coupled Rossler systems. 4.3. Linear stability analysis. 4.4. One-parameter bifurcation diagrams. 4.5. Emergence of quasiperiodicity in coupled logistic maps. 4.6. Two-parameter phase diagrams. 4.7. Lyapunov exponents and hyperchaos. 4.8. Symmetrically coupled systems of differential equations. 4.9. Hopf bifurcation of the antiphase solution. 4.10. The first bifurcation is a period-doubling bifurcation. 4.11. Conclusion -- 5. Chaos in technical control systems. 5.1. Limits to linear analysis. 5.2. Two coupled thermostatically controlled radiators. 5.3. Mode-locking between the radiator systems. 5.4. Nonlinear dynamics of a thrust vectored aircraft. 5.5. Stability of the equilibrium point. 5.6. Forcing of the thrust deflection. 5.7. Conclusion -- 6. Ecological and microbiological population dynamics. 6.1. Chaos in ecological systems. 6.2. The food-web model. 6.3. Multi-species model of bacterium-phage interaction. 6.4. The chaotic hierarchy. 6.5. Spatial inhomogeneity and diffusive coupling -- 7. Physiological control systems. 7.1. Chaos and life. 7.2. Nephron pressure and flow regulation. 7.3. Model of nephron autoregulation. 7.4. Bifurcation structure for the nephron model. 7.5. Experimental verification and dimension calculations. 7.6. Pulsatile insulin secretion -- 8. Chaos and hyperchaos in economic and managerial systems. 8.1. What will the stock prices be tomorrow? 8.2. Nonlinear phenomena in the economy. 8.3. The economic long wave. 8.4. The model. 8.5. Mode-locking. 8.6. The beer game. 8.7. The ordering heuristics. 8.8. Experimental results. 8.9. The simulation model. 8.10. Simulation results -- 9. Spatiotemporal phenomena in extended systems. 9.1. Extensions to higher dimensions. 9.2. Mode-locking in periodically driven Gunn diodes. 9.3. The chemical basis of morphogenesis. 9.4. Pattern formation in a chemical reaction-diffusion system. 9.5. Bifurcation diagrams and basic turing structures. 9.6. Mode competition and front propagation. |