Modeling and Computations in Dynamical Systems : In Commemoration of the 100th Anniversary of the Birth of John Von Neumann.
Başlık:
Modeling and Computations in Dynamical Systems : In Commemoration of the 100th Anniversary of the Birth of John Von Neumann.
Yazar:
Doedel, Eusebius J.
ISBN:
9789812774569
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (357 pages)
Seri:
World Scientific Series on Nonlinear Science Series B ; v.13
World Scientific Series on Nonlinear Science Series B
İçerik:
CONTENTS -- Editorial -- Transport in Dynamical Astronomy and Multibody Problems -- 1. Introduction -- 2. Description of the PCR3BP Global Dynamics -- 3. Computing Transport -- 4. Example: The Sun-Jupiter-Asteroid System -- 5. Conclusions and Future Directions -- A Brief Survey on the Numerical Dynamics for Functional Differential Equations -- 1. Introduction -- 2. Discretization as a Family of Approximating Discrete-Time Semidynamical Systems -- 3. Qualitative Numerics for Delay Equations -- 4. Remarks on Functional Differential Equations -- Bifurcations and Continuous Transitions of Attractors in Autonomous and Nonautcnomcus Systems -- 1. Introduction -- 2. Autonomous Systems -- 3. Nonautonomous Systems -- 4. A Total Stability Theorem -- 5. Applications of the Total Stability Theorem -- 6. Concluding Remarks and Questions -- A. Appendix: Proof of Theorem 1 -- A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields -- 1. Introduction -- 2. Approximation by Geodesic Level Sets -- 3. BVP Continuation of Trajectories -- 4. Computation of Fat Trajectories -- 5. PDE Formulation -- 6. Box Covering -- 7. Discussion -- Commutators of Skew-Symmetric Matrices -- 1. Norms and Commutators in Mn[R] and sO(n) -- 2. The Reduced Commutator Matrix in so(n) -- 3. The Radius of so(n) for n > 4 -- 4. Conclusion -- Simple Neural Networks that Optimize Decisions -- 1. Introduction -- 2. Models of Decision Tasks -- 3. Optimal Signal Discrimination in the One-Dimensional Models -- 4. The Locus Coeruleus Brainstem Area and Optimal Gain Trajectories -- 5. Discussion and Conclusions -- Newton Flow and Interior Point Methods in Linear Programming -- 1. Introduction -- 2. The Central Path is a Trajectory of the Newton Vector Field -- 3. An Analytic Expression for the Newton Vector Field -- 4. Extension to the Faces of p.
5. Analyticity and Derivatives -- 6. Example -- Numerical Continuation of Branch Points of Equilibria and Periodic Orbits -- 1. Introduction -- 2. Equilibria and their Branch Points -- 3. Periodic Solutions and their Branch Points -- 4. Numerical Detection Computation and Continuation of Branch Points of Periodic Solutions -- 5. Example 1: The A -> B -> C Reaction -- 6. Example 2: An Electronic Circuit -- Coarse-Grained Observation of Discretized Maps -- 1. Introduction -- 2. Definitions and Assumptions -- 3. The Main Result: The Conditions for Am =BMN -- 4. Application of the Coarse-Grained Model -- 5. Summary and Related Topics -- Multiple Helical Perversions of Finite Intristically Curved Rods -- 1. Introduction -- 2. Analysis -- 3. Global Computations and their Interpretation -- 4. Summary and Related Issues -- Bifurcations of Stable Sets in Noninvertible Planar Maps -- 1. Introduction -- 2. Example -- 3. Generic Codimension-One Bifurcations of Stable Sets -- 4. Bifurcations of Basin Boundaries -- 5. Stable Set versus Unstable Manifold -- 6. Conclusions -- Multiparametric Bifurcations in an Enzyme-Catalyzed Reaction Model -- 1. Introduction -- 2. Codimension-One and -Two Bifurcations of Equilibria -- 3. Degenerate Bogdanov-Takens Bifurcations -- 4. Homoclinic Orbits and Their Numerical Continuation -- 5. Homoclinic Bifurcations in the Enzyme System -- 6. Bifurcation Sets -- 7. Conclusions -- Straightforward Computation of Spatial Equilibria of Geometrically Exact Cosserat Rods -- 1. Introduction -- 2. Formulation -- 3. Numerical Implementation -- 4. Examples -- 5. Concluding Remarks -- Multiparameter Parallel Search Branch Switching -- 1. Background and Basic Result -- 2. Statement of the Algorithm -- 3. Examples.
Equation-Free Effective Computation for Discrete Systems: A Time Stepper Based Approach -- 1. Introduction -- 2. A Coarse Time Stepper for Discrete Systems -- 3. A Discrete Traveling Front Example -- 4. Numerical Results -- 5. An Alternative Continuum Approach: Pade Approximations -- 6. Summary and Discussion -- Model Reduction for Fluids Using Balanced Proper Orthogonal Decomposition -- 1. Introduction -- 2. Background on Model Reduction -- 3. Balanced POD -- 4. Example: Linearized Channel Flow -- 5. Conclusions -- Appendix A Theorems on Computing Balancing Transformations -- Bifurcation Tracking Algorithms and Software for Large Scale Applications -- 1. Introduction -- 2. Bifurcation Tracking Algorithms -- 3. Bifurcation Analysis of Rayleigh-Benard Convection in a 5 x 5 x 1 Box -- 4. Summary and Conclusions -- An Algorithm for Finding Invariant Algebraic Curves of a Given Degree for Polynomial Planar Vector Fields -- 1. Introduction and Preliminary Definitions -- 2. The Problem of Invariant Algebraic Curves from the Point of View of Linear Algebra -- 3. The Algorithm -- 4. Examples -- Author Index.
Özet:
The Hungarian born mathematical genius, John von Neumann, was undoubtedly one of the greatest and most influential scientific minds of the 20th century. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J E Marsden, P J Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this book offers a unique combination of theoretical and applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics. The contents of this book was also published as a special issue of the International Journal of Bifurcation and Chaos - March 2005 . Sample Chapter(s). Chapter 1: Transport in Dynamical Astronomy and Multibody Problems (2,676 KB). Contents: Transport in Dynamical Astronomy and Multibody Problems (M Dellnitz et al.); A Brief Survey on the Numerical Dynamics for Functional Differential Equations (B M Garay); Bifurcations and Continuous Transitions of Attractors in Autonomous and Nonautonomous Systems (P E Kloeden & S Siegmund); A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields (B Krauskopf et al.); Commutators of Skew-Symmetric Matrices (A M Bloch & A Iserles); Simple Neural Networks that Optimize Decisions (E Brown et al.); Newton Flow and Interior Point Methods in Linear Programming (J-P Dedieu & M Shub); Numerical Continuation of Branch Points of Equilibria and Periodic Orbits (E J Doedel et al.); Coarse-Grained Observation of Discretized Maps (G Domokos); Multiple Helical Perversions of Finite, Intristically Curved Rods (G Domokos & T J Healey); Bifurcations of Stable
Sets in Noninvertible Planar Maps (J P England et al.); Multiparametric Bifurcations in an Enzyme-Catalyzed Reaction Model (E Freire et al.); Straightforward Computation of Spatial Equilibria of Geometrically Exact Cosserat Rods (T J Healey & P G Mehta); Multiparameter Parallel Search Branch Switching (M E Henderson); Equation-Free, Effective Computation for Discrete Systems: A Time Stepper Based Approach (J Möller et al.); Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition (C W Rowley); Bifurcation Tracking Algorithms and Software for Large Scale Applications (A G Salinger et al.); An Algorithm for Finding Invariant Algebraic Curves of a Given Degree for Polynomial Planar Vector Fields (G Swirszcz). Readership: Graduate students and scientists interested in applied and computational mathematics, dynamical systems, mechanics and related areas.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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